NLN NEX MATH PRACTICE TEST
Sharpen quantitative reasoning skills with structured practice covering the core math concepts required for nursing program admission.
Topics Covered
Whole numbers and basic operations
Fractions and mixed numbers
Decimals and rounding
Ratios and proportions
Percentages
Word problem interpretation
Target: 30
min
00:00
Score
0 /
0
Correct
Wrong
Remaining
Question 1 / 31
897.54-48.39 =
A.
849.15
B. 813.15
C. 859.15
D. 814.15
Rationale
When subtracting 48.39 from 897.54, the final result is 849.15, but reaching this value requires a careful, structured approach rather than quick mental subtraction. Because both numbers contain decimal places extending to the hundredths, the decimal points must first be aligned. This alignment ensures that values in the hundredths, tenths, ones, tens, and hundreds places are compared correctly and prevents place-value errors.
After aligning the decimals, subtraction proceeds from right to left. In the hundredths column, 9 hundredths cannot be subtracted from 4 hundredths without borrowing. Borrowing is therefore required from the tenths column, and in turn, additional borrowing may be required from the ones and tens columns. Each borrowing step must be tracked carefully so that no place value is altered incorrectly. When this process is completed methodically across all columns, the resulting difference is 849.15.
This answer also makes sense conceptually. Since 48.39 is slightly less than 50, subtracting it from a number close to 900 should give a result slightly greater than 850. Any answer far below or far above this range signals a likely arithmetic error.
A. 849.15
It represents the correct and fully justified result of the subtraction. It reflects that the decimal points were aligned correctly before subtracting, that borrowing was handled properly across multiple place values, and that each column was subtracted in the correct order.
In addition, this value passes a strong reasonableness check. Subtracting approximately 50 from approximately 900 gives an estimated answer of about 850, which closely matches 849.15. Because both the exact calculation and estimation support this value, It is mathematically sound and reliable.
B. 813.15
This value is far too low to be the correct answer and indicates that an excessive amount was subtracted. Students often arrive at this result when borrowing is done incorrectly or when digits are subtracted from the wrong place values.
A common mistake that produces this answer is subtracting the digits correctly in one column but failing to adjust the remaining columns after borrowing. Another possibility is confusing 48.39 with a larger number, such as 84.39, which would drastically reduce the result. When the subtraction is reworked carefully with proper alignment and borrowing, this value does not appear.
C. 859.15
It is too high and suggests that the subtraction was incomplete. Errors leading to this result often involve skipping a borrowing step in the decimal portion or subtracting a smaller value than intended.
For example, a student might subtract 38.39 instead of 48.39 or fail to borrow correctly from the ones place when subtracting the tenths. While this value may seem reasonable at first glance, it does not match the true difference once all subtraction steps are performed accurately.
D. 814.15
This answer reflects a significant place-value error. It typically occurs when decimals are misaligned or when borrowing is mishandled across more than one column. In some cases, students subtract digits vertically without ensuring that tenths align with tenths and hundredths align with hundredths, leading to a distorted result.
When the subtraction is set up correctly and solved step by step, there is no point at which this value emerges, confirming that it does not represent a valid solution.
Conclusion
Accurate decimal subtraction depends on three essential principles: aligning decimal points, borrowing correctly across place values, and subtracting systematically from right to left. When these principles are applied to 897.54-48.39, the calculation leads consistently to 849.15.
A comparison of all answer choices shows that only option A satisfies the exact arithmetic, aligns with logical estimation, and reflects correct handling of place value. Therefore, 849.15 is the only defensible and correct result.
Question 2 / 31
94.31 + 973.37 =
A.
1067.68
B. 1167.68
C. 1067.78
D. 1167.78
Rationale
Adding 94.31 and 973.37 produces a total of 1067.68, but this result is only reached when the addition is set up correctly and carried out with careful attention to decimal alignment and carrying. Because both numbers include hundredths, the decimal points must first be aligned so that hundredths are added to hundredths and tenths to tenths. Failing to align decimals is one of the most common causes of error in decimal addition.
Once aligned, the addition begins in the hundredths column. The hundredths add to produce a value that requires carrying into the tenths column. This carry must then be included when adding the tenths place. As the addition continues into the ones and tens places, any carry generated must be transferred correctly to the next column. When each of these steps is followed carefully, the final sum is 1067.68.
This answer also makes sense when using estimation. Since 94.31 is close to 100 and 973.37 is close to 973, the sum should be slightly above 1070 or just below it. An answer near 1067 is therefore reasonable, while answers near 1167 indicate an obvious error.
1067.68
It reflects correct decimal alignment, proper carrying from the decimal portion into the whole-number portion, and accurate addition of each place value. The calculation remains consistent from the hundredths place through the thousands place. In addition, the size of the result aligns with estimation, confirming that no extra digits were added or omitted. This makes 1067.68 the only mathematically sound answer.
B. 1167.68
This value is too large by exactly 100, indicating a major place-value error. A result like this typically occurs when an extra hundred is mistakenly added during the calculation. Common causes include misreading 94.31 as 194.31 or incorrectly carrying into the hundreds column. While the decimal portion appears correct, the inflated whole-number portion shows that the addition was not handled properly.
C. 1067.78
It is close to the correct answer but contains a decimal error. It usually results from adding the hundredths place incorrectly or applying a carry where none is needed. Even a small mistake in the decimal portion changes the final sum and makes this answer incorrect. Proper addition of the hundredths and tenths places does not yield this value.
D. 1167.78
This value reflects multiple errors. The increase of 100 indicates an incorrect carry or misreading of one of the numbers, while the incorrect decimal portion suggests an additional error in adding the hundredths or tenths places. When both the decimal and whole-number portions are incorrect, the result deviates significantly from the true sum.
Conclusion
Correct decimal addition requires aligning decimal points, adding systematically from right to left, and carrying accurately between place values. When 94.31 and 973.37 are added following these rules, the result is 1067.68. Reviewing all answer choices shows that only option A satisfies correct arithmetic, proper place-value handling, and logical estimation.
Question 3 / 31
Using the following equation solve for (x): 3x-4y = 25, where y = 2
A.
x = 10
B. x = 11
C. x = 12
D. x = 13
Rationale
The value of x is 11 when the equation is solved correctly after substituting the given value of y. Solving equations with two variables becomes much simpler once one variable is provided, because it allows the equation to be rewritten using only a single unknown.
The first step is to substitute y = 2 into the equation:
3x-4(2) = 25
Next, simplify the multiplication:
3x-8 = 25
To isolate x, add 8 to both sides of the equation:
3x = 33
Finally, divide both sides by 3:
x = 11
Each step follows standard algebraic rules, and the operations are applied consistently to both sides of the equation.
A. x = 10
This value does not satisfy the equation when substituted back in. Replacing x with 10 gives:
3(10)-4(2) = 30-8 = 22
Since 22 does not equal 25, this value does not solve the equation. Students often arrive at this answer by stopping too early or making a small arithmetic error when isolating x.
B. x = 11
This value satisfies the equation exactly. Substituting x = 11 back into the original equation gives:
3(11)-4(2) = 33-8 = 25
Because the left side equals the right side, this confirms that x = 11 is the correct solution.
C. x = 12
This value results in a number greater than 25 when substituted:
3(12)-4(2) = 36-8 = 28
This indicates that the value of x is too large. Such an answer often comes from adding instead of subtracting during the simplification step.
D. x = 13
It produces an even larger value:
3(13)-4(2) = 39-8 = 31
Because the result is much greater than 25, this value clearly does not satisfy the equation. It reflects a failure to isolate x correctly or a misunderstanding of how substitution works.
Conclusion
Solving equations with substitution requires replacing the known variable first, simplifying the equation, and then isolating the remaining variable step by step. When y = 2 is substituted into 3x-4y = 25 and the equation is solved correctly, the solution is x = 11. Checking all answer choices confirms that B is the only value that satisfies the original equation.
Question 4 / 31
894 + ((3)(12)) =
A.
730
B. 932
C. 930
D. 945
Rationale
The value of the expression 894 + ((3)(12)) is 930 when the order of operations is applied correctly. This problem tests understanding of grouping symbols and multiplication before addition, which is a foundational arithmetic concept.
The expression contains parentheses, so the calculation inside the parentheses must be completed first. The inner operation is the multiplication of 3 and 12. Performing that multiplication gives a product of 36. Once the multiplication inside the parentheses is completed, the expression becomes:
894 + 36
This final addition is straightforward. Adding 36 to 894 increases the value first to 900 and then by an additional 30, and finally by 6, resulting in a total of 930. Because all steps follow the correct order of operations, this result is reliable.
This answer also makes sense conceptually. Adding a relatively small number like 36 to a number close to 900 should result in a value slightly above 900, not dramatically lower or higher.
A. 730
This value is far too low and reflects a serious misunderstanding of the problem. A result like this often occurs when the multiplication inside the parentheses is ignored entirely or when subtraction is mistakenly used instead of addition. Because the original expression adds a positive quantity to 894, the result cannot be smaller than 894, making It clearly incorrect.
B. 932
This value is close to the correct answer but still incorrect. It typically results from a small arithmetic error after the multiplication step, such as miscalculating 3 X 12 or incorrectly adding the product to 894. While the result is in a reasonable range, careful recalculation shows that the final sum does not reach 932.
C. 930
It correctly reflects both steps of the calculation: first multiplying 3 and 12 to obtain 36, and then adding that value to 894. The arithmetic is accurate, and the result aligns with estimation and logical reasoning. Because all operations are applied correctly and in the proper order, this is the correct answer.
D. 945
This value is too high and usually results from overestimating the product of 3 and 12 or adding an incorrect value to 894. In some cases, students may mistakenly treat the multiplication as producing a larger number or may add an extra ten during the final addition. Because the increase from 894 should only be 36, this result is not valid.
Conclusion
Expressions containing parentheses must be simplified by completing the operations inside the grouping symbols first. In this problem, multiplying 3 by 12 produces 36, which is then added to 894. Following the correct order of operations leads to a final result of 930. A review of all answer choices confirms that C is the only option that reflects correct arithmetic and logical reasoning.
Question 5 / 31
Round to the nearest two decimal places: 9.42? 3.47
A.
2.63
B. 2.71
C. 2.81
D. 2.94
Rationale
To determine the value of 9.42÷ 3.47, the division must be carried out carefully, followed by rounding to two decimal places. Because both numbers contain decimals, the division often produces a longer decimal that must be rounded appropriately.
Performing the division yields a quotient of approximately 2.714€¦. Since the problem requires rounding to two decimal places, attention is focused on the third decimal place. In this case, the third decimal digit is 4, which is less than 5. Therefore, the second decimal place remains unchanged.
As a result, the value rounds to 2.71.
This answer also makes sense when estimating. Dividing a number slightly less than 10 by a number slightly greater than 3 should give a result slightly under 3. A value around 2.7 fits this expectation well.
A. 2.63
This value is too low and usually results from truncating the decimal instead of rounding or from an arithmetic error during division. While it may appear close, it does not reflect the correct quotient of the division.
B. 2.71
It accurately represents the quotient of 9.42÷ 3.47 rounded to two decimal places. The division is performed correctly, and the rounding rule is applied properly based on the third decimal digit. The value also aligns with logical estimation, confirming it as correct.
C. 2.81
This value is too high and often results from rounding incorrectly, such as rounding up when the third decimal digit does not justify it. It may also come from a miscalculation during long division. Because the true quotient is closer to 2.71 than 2.81, It is invalid.
D. 2.94
It reflects a significant division error. It suggests that the divisor was treated as smaller than it actually is or that the decimal point was misplaced. Since 3.47 is close to 3.5, a quotient near 3 would only be expected if the numerator were much larger.
Conclusion
Dividing decimals requires careful calculation followed by correct rounding based on the appropriate decimal place. When 9.42 is divided by 3.47, the quotient is approximately 2.714€¦, which rounds to 2.71. Evaluating all answer choices confirms that B is the only option consistent with correct division, rounding rules, and estimation.
Question 6 / 31
0.10 equals which of the following fractions?
A.
1/100
B. 1/10
C. 1/50
D. 01-May
Rationale
The decimal 0.10 is equal to the fraction 1/10. Understanding this conversion requires recognizing what a decimal represents in terms of place value. The decimal 0.10 means ten hundredths, which can be written as the fraction 10/100. When this fraction is simplified by dividing both the numerator and denominator by 10, it becomes 1/10.
Another way to see this relationship is by recognizing that 0.1 and 0.10 represent the same value. Adding a zero to the right of a decimal does not change its value, just as 1/10 and 10/100 represent the same quantity. Therefore, the correct fractional form of 0.10 is 1/10.
This also makes sense intuitively. One tenth represents a value larger than one hundredth but smaller than one fifth, placing it exactly between those quantities.
A. 1/100
This fraction equals 0.01, not 0.10. It represents one hundredth, which is ten times smaller than one tenth. It is often chosen when students focus on the number of digits in the decimal rather than the actual place value. Because 0.10 is significantly larger than 0.01, It is incorrect.
B. 1/10
This fraction correctly represents the value of 0.10. One tenth written as a decimal is 0.1, which is mathematically equivalent to 0.10. The fraction and decimal describe the same quantity using different formats, making this the correct choice.
C. 1/50
This fraction equals 0.02, which is much smaller than 0.10. Errors leading to It often come from guessing or misunderstanding how to convert between decimals and fractions. Because 1/50 does not simplify to a value close to one tenth, it cannot be correct.
D. 1/5
This fraction equals 0.20, which is twice as large as 0.10. Students sometimes confuse one tenth with one fifth because both are common fractions, but their decimal values are different. Since 0.20 is clearly larger than 0.10, It is incorrect.
Conclusion
Decimals and fractions are two ways of expressing the same values. The decimal 0.10 represents ten hundredths, which simplifies to the fraction 1/10. Comparing all answer choices confirms that B is the only fraction that accurately represents the value of 0.10.
Question 7 / 31
If one side of a triangle equals 4 inches and the second side equals 5 inches what does the third side equal?
A.
9 inches
B. 1 inch
C. 6.4 inches
D. 4.6 inches
Rationale
The third side of the triangle is 6.4 inches, determined using the Pythagorean Theorem, which applies to right triangles. The theorem states that for a right triangle with legs a and b, and hypotenuse c:
a² + b² = c²
In this problem, the two given sides are 4 inches and 5 inches. Squaring each value gives:
4² = 16
5² = 25
Add the squares:
16 + 25 = 41
Now take the square root of 41 to find the length of the third side:
ˆš41 ‰ˆ 6.4 inches
This value is reasonable because the hypotenuse of a right triangle must always be longer than either leg, but shorter than their sum.
A. 9 inches
This value equals the sum of the two given sides (4 + 5), which violates triangle geometry. The third side of a triangle must be less than the sum of the other two sides. It typically results from adding the side lengths instead of applying the Pythagorean Theorem.
B. 1 inch
This value is far too small and does not satisfy triangle inequality rules. A triangle with sides 4, 5, and 1 inches cannot exist because the sum of the smaller sides would not exceed the largest side. It reflects a misunderstanding of triangle properties.
C. 6.4 inches
It correctly applies the Pythagorean Theorem. The calculation is mathematically sound, and the resulting value fits all geometric constraints of a right triangle. It is greater than both given sides but less than their sum, confirming its validity.
D. 4.6 inches
This value may come from averaging or guessing rather than using the correct formula. While it is larger than one of the sides, it is not large enough to be the hypotenuse of a right triangle with sides 4 and 5 inches. It does not satisfy the Pythagorean relationship.
Conclusion
For right triangles, the Pythagorean Theorem provides the correct method for finding a missing side. When sides of 4 inches and 5 inches are given, squaring, adding, and taking the square root results in a third side of 6.4 inches. Evaluating all answer choices confirms that C is the only option consistent with correct geometry and mathematical reasoning.
Question 8 / 31
If a = 4 and b = 5 then a(a? + b) =
A.
52
B. 84
C. 62
D. 64
Rationale
To correctly evaluate the expression a(a² + b), it is essential to substitute the given values and apply the order of operations carefully, paying close attention to exponents and grouping symbols.
First, substitute the given values:
a = 4
b = 5
The expression becomes:
a(a² + b) = 4(4² + 5)
The exponent must be evaluated first:
4² = 16
Now substitute back into the parentheses:
4(16 + 5)
Next, perform the addition inside the parentheses:
16 + 5 = 21
Finally, multiply:
4 X 21 = 84
This final value represents the correct evaluation of the original expression.
A. 52
This value typically results from an incorrect order of operations. A common mistake is adding a and b first or partially evaluating the expression, such as calculating 4² = 16 and then adding 36 incorrectly, or multiplying before completing the entire expression inside the parentheses. Because the grouped expression was not fully evaluated before multiplication, It is incorrect.
B. 84
It reflects the correct application of algebraic rules. The exponent is evaluated first, the terms inside the parentheses are added correctly, and the multiplication by a is performed last. The step-by-step process is mathematically sound, making this the correct answer.
C. 62
This result often occurs when the square of a is miscalculated or when the student multiplies a² by a and then adds b afterward, rather than treating (a² + b) as a grouped expression. Because this does not follow the structure of the original expression, It is incorrect.
D. 64
This value reflects squaring a and ignoring b entirely, or mistakenly treating the expression as a² X a without adding b. Since the problem clearly includes b inside the parentheses, omitting it leads to an incomplete and incorrect result.
Conclusion
Expressions involving exponents and parentheses must be solved in a specific order: exponents first, then operations inside parentheses, and finally multiplication. Applying these rules correctly gives a final value of 84, confirming B as the only correct answer.
Question 9 / 31
8 ? + 6 ? =
A.
32
B. 15 ?
C. 14 ?
D. 17 ?
Rationale
The sum of 8 ¾ and 6 ½ is 15 ¼.
To correctly add mixed numbers, both the whole-number parts and the fractional parts must be handled carefully and combined at the end.
Start by separating the mixed numbers into whole numbers and fractions:
8 ¾ = 8 + ¾
6 ½ = 6 + ½
Now add the whole numbers first:
8 + 6 = 14
Next, add the fractional parts:
¾ + ½
Because these fractions have different denominators, they must be rewritten using a common denominator.
The least common denominator of 4 and 2 is 4.
¾ stays as ¾
½ = 2/4
Now add:
¾ + 2/4 = 5/4
Since 5/4 is an improper fraction, it must be rewritten as a mixed number:
5/4 = 1 ¼
Finally, combine this result with the whole-number sum:
14 + 1 ¼ = 15 ¼
A. 32
It is far too large and does not reflect proper addition of mixed numbers. It suggests that the values were multiplied or added incorrectly without separating whole numbers and fractions.
B. 15 ¼
It correctly reflects the result of adding the whole-number portions first and then properly converting and adding the fractional parts. The final sum is accurate and reasonable based on the original values.
C. 14 ½
This value is too small and typically results from adding only the fractions and failing to correctly account for the extra whole number created when 5/4 is converted to a mixed number.
D. 17 ¾
It is too large and usually results from incorrectly adding the fractions as ¾ + ½ = 1 ¼ and then adding that incorrectly to the whole numbers.
Conclusion
By separating the mixed numbers, finding a common denominator, and properly converting the improper fraction, the correct sum is 15 ¼. Option B is the only answer that matches this complete and accurate process.
Question 10 / 31
10b = 5a-15. If a = 3 then b =
A.
7
B. 5
C. 1
D. 0
Rationale
The value of b is 0 when a equals 3.
Begin by substituting the given value of a directly into the equation:
10b = 5a-15
Replace a with 3:
10b = 5(3)-15
Now evaluate the right side of the equation step by step:
5 X 3 = 15
15-15 = 0
So the equation becomes:
10b = 0
Next, isolate b by dividing both sides by 10:
b = 0÷ 10
b = 0
A. 7
It would require the right side of the equation to equal 70, which is not supported by the arithmetic. It suggests that subtraction was ignored or the equation was not simplified correctly.
B. 5
This value would imply that 10b equals 50, but after substitution and simplification, the right side of the equation equals 0, not 50.
C. 1
It results from stopping the calculation too early or incorrectly dividing before fully simplifying the expression on the right side.
D. 0
It correctly reflects the result of substituting a = 3, simplifying the equation, and solving for b. It satisfies the equation exactly.
Conclusion
After substituting the given value, simplifying the expression, and isolating the variable, the solution is b = 0. Option D is the only answer that correctly follows each step of the equation.
Question 11 / 31
12 members of a weight loss club are female; there are 23 members altogether. Approximately what percentage of members are males?
A.
59%
B. 48%
C. 36%
D. 44%
Rationale
Approximately 48% of the members are males. The key idea in this question is that the total number of members includes both females and males, so you must first determine how many members are male before you can convert that value into a percentage of the total group.
Since 12 members are female and there are 23 members altogether, the number of male members is found by subtracting females from the total. That calculation is 23 minus 12, which equals 11. This means there are 11 males in the club. To find the percentage of members who are male, the male portion is compared to the total membership by forming the fraction 11 out of 23. Converting 11/23 to a decimal gives approximately 0.478. When this decimal is multiplied by 100, it becomes approximately 47.8%, which rounds to 48%. This matches the idea of "approximately" in the question, meaning a rounded percentage is expected.
A quick reasonableness check also supports this. If 12 out of 23 are female, females make up slightly more than half of the club. That means males must make up slightly less than half, and 48% fits that expectation well.
A. 59%
This percentage is too high to be the male portion in this situation. If males were 59% of the group, then males would represent more than half the club. But the problem states 12 females out of 23 total, and 12 is already more than half of 23 (since half of 23 is 11.5). Because females are the majority, males cannot be 59%. It commonly appears when someone mistakenly uses the female number as the "male" number or subtracts in the wrong direction.
B. 48%
It correctly represents the male proportion of the club. After finding that there are 11 males (23 total minus 12 females), dividing 11 by 23 produces approximately 0.478, which becomes about 47.8%. Rounding gives 48%, which is exactly what "approximately" calls for. This result also fits the situation logically because the male group is slightly smaller than the female group, so the male percentage should be slightly less than 50%.
C. 36%
This percentage is too low to represent the male portion. A 36% male membership would mean just over one-third of the members are male. But 11 out of 23 is close to one-half, not one-third. This answer can result from dividing by the wrong number, using the female count as the denominator, or doing an incorrect rounding step.
D. 44%
This is closer than some other wrong options, but it still does not match the correct proportion. If you calculate 11/23 accurately, you get approximately 47.8%, not 44%. This choice often comes from rough guessing, rounding too early, or using an incorrect estimate such as assuming 11/25 instead of 11/23.
Conclusion
To find the percentage of males, first subtract females from the total to get the male count: 23-12 = 11 males. Then convert 11 out of 23 into a percent: 11/23 ‰ˆ 0.478, or about 47.8%, which rounds to 48%. Therefore, B is the only option that correctly represents the approximate male percentage.
Question 12 / 31
A student invests $3000 of his student loan and receives 400 dollars in interest over a 4-year period. What is his average yearly interest rate?
A.
3.30%
B. 2.10%
C. 5%
D. 4.20%
Rationale
The student's average yearly interest rate is approximately 3.3%. This problem requires determining how much interest was earned per year on average and then expressing that yearly interest as a percentage of the original investment.
The total interest earned over the entire period is $400, and the time span is 4 years. To find the average interest earned each year, divide the total interest by the number of years. This gives 400÷ 4 = 100. This means the investment generated an average of $100 in interest per year.
Next, convert this yearly interest into a percentage of the principal. The original investment was $3000. Dividing the yearly interest by the principal gives 100÷ 3000 = 0.03333€¦. Converting this decimal to a percentage results in 3.33%, which rounds to 3.3%.
This answer is reasonable when checked logically. One percent of $3000 is $30, so three percent would be $90. An interest rate slightly above 3% should therefore yield about $100 per year, which aligns perfectly with the calculated result.
A. 3.3%
It correctly represents the average yearly interest rate. The student earns $100 per year on a $3000 investment, and $100 divided by $3000 equals 0.0333€¦, or 3.3%. Both the calculation and the logical estimate confirm this answer.
B. 2.1%
This rate is too low. At 2.1%, the yearly interest on $3000 would be about $63. Over four years, that would total roughly $252, which is far less than the stated $400. It typically results from failing to correctly relate the interest to the time period.
C. 5%
This rate is too high. A 5% yearly return on $3000 would generate $150 per year, resulting in $600 over four years. This exceeds the given total interest, showing that It overestimates the rate.
D. 4.2%
It is also too high. A 4.2% yearly rate would produce about $126 per year, totaling approximately $504 over four years. Since the actual interest earned was only $400, this percentage does not fit the data.
Conclusion
The student earned $400 in interest over 4 years, which averages to $100 per year. Dividing $100 by the original $3000 investment gives an annual rate of about 3.3%. Therefore, A (3.3%) is the only option that correctly represents the average yearly interest rate.
Question 13 / 31
A can has a radius of 1.5 inches and a height of 3 inches. Which of the following best represents the volume of the can?
A.
17.2 in?
B. 19.4 in?
C. 21.2 in?
D. 23.4 in?
Rationale
The volume of a can is found using the formula for the volume of a cylinder, which is volume equals π multiplied by the radius squared and then multiplied by the height. In this problem, the radius is 1.5 inches and the height is 3 inches. The first step is squaring the radius. Squaring 1.5 gives 2.25. This value is then multiplied by the height, giving 2.25 X 3 = 6.75. Finally, this result is multiplied by π. Using an approximation of π as 3.14, the calculation becomes 6.75 X 3.14, which equals approximately 21.2 cubic inches.
This value represents the space inside the can and is consistent with the dimensions given. The question asks for the best representation, which means a close approximation is acceptable.
A. 17.2 in³
This value is too small to represent the volume of the can. Using the correct formula and substituting the given radius and height produces a result well above 17 cubic inches. This answer would likely result from omitting π or incorrectly squaring the radius.
B. 19.4 in³
It is closer but still incorrect. It suggests that part of the formula was used properly, but either π was rounded too low or one of the steps in the calculation was misapplied. The correct calculation yields a larger value.
C. 21.2 in³
This value matches the result obtained when the radius and height are correctly substituted into the cylinder volume formula and π is applied appropriately. It also makes sense when estimating, since a radius of 1.5 inches and height of 3 inches would reasonably produce a volume just over 20 cubic inches.
D. 23.4 in³
This value is too large and suggests an overestimation, possibly from rounding π too high or incorrectly multiplying the components of the formula.
Conclusion
By correctly applying the formula for the volume of a cylinder and carefully carrying out each step, the volume of the can is approximately 21.2 cubic inches. Therefore, C (21.2 in³) is the correct answer.
Question 14 / 31
Which number is represented by the Roman numeral XXVII?
A.
47
B. 72
C. 32
D. 27
Rationale
The Roman numeral XXVII represents the value 27 when each symbol is interpreted according to standard Roman numeral rules and combined correctly.
A. 47
A full step-by-step calculation leads to 27, not 47. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 72
72 does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 27, not 72. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 32
32 does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 27, not 32. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 27
It aligns with the correct computation for the question and matches the final value 27. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
Conclusion
Carefully applying the Roman numeral rules and verifying the result against the answer choices confirms that the correct value is 27.
Question 15 / 31
Dawn has a 20% off one shirt coupon at her favorite store. If she buys 3 shirts at $29.99 each and uses her coupon how much will her total bill be? Round to the nearest hundredth.
A.
$71.98
B. $83.97
C. $86.42
D. $89.97
Rationale
The total cost is found by first calculating the full price of the three shirts and then applying the 20% discount to reduce that total accordingly.
A 20% discount on one shirt means you subtract 20% of one shirt's price from the original total for three shirts.
A. $71.98
This choice does not match what the question is asking for. When you apply the required method carefully, you land on $86.42 rather than $71.98. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
B. $83.97
Three shirts cost 3 x $29.99 = $89.97. A 20% discount on one shirt is 0.20 x $29.99 = $5.998. Subtracting that discount from the total gives $89.97 -$5.998 = $83.972, which rounds to $83.97. This matches how retail totals are reported: to the nearest cent.
C. $86.42
This choice does not match what the question is asking for. When you apply the required method carefully, you land on $86.42 rather than $86.42. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
D. $89.97
This choice does not match what the question is asking for. When you apply the required method carefully, you land on $86.42 rather than $89.97. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
Conclusion
Therefore, after correctly applying the discount and rounding to the nearest hundredth, the final total Dawn pays is $86.42.
Question 16 / 31
|7| + |-2| = ____ Note: This problem shows the number -2 within an absolute value sign not the number -21.
A.
5
B. 0
C. 14
D. 9
Rationale
The absolute value of a number represents its distance from zero, so both |7| and |-2| are evaluated as positive values before being added together.
A. 5
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 14, not 5. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 0
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 14, not 0. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 14
It aligns with the correct computation for the question and matches the final value 14. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
D. 9
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 14, not 9. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
When each absolute value is evaluated correctly and the results are combined, the final value is 14.
Question 17 / 31
12.5 x 24.6 = ?
A.
327.3
B. 366.5
C. 307.5
D. 308.7
Rationale
12.5 x 24.6 = 307.5
A. 327.3
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 307.5, not 327.3. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 366.5
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 307.5, not 366.5. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 307.5
It aligns with the correct computation for the question and matches the final value 307.5. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
D. 308.7
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 307.5, not 308.7. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
Placing the decimal correctly after multiplication gives a final product of 307.5.
Question 18 / 31
Which number is in the hundredths place in 0.5983?
A.
5
B. 8
C. 3
D. 9
Rationale
9 is in the hundredths place of 0.5983
9 is the correct answer to the question: Which number is in the hundredths place in 0.5983?
A. 5
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 9, not 5. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 8
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 9, not 8. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 3
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 9, not 3. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 9
It aligns with the correct computation for the question and matches the final value 9. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
Conclusion
Reading 0.5983 by place value shows that 5 is in the tenths place and 9 is in the hundredths place, so the correct digit in the hundredths position is 9.
Question 19 / 31
Reduce 72/108
A.
6/9
B. 1/3
C. 72/108
D. 2/3
Rationale
2/3 is the correct answer to the question: Reduce 72/108
Reducing a fraction means dividing numerator and denominator by their greatest common factor so the ratio stays the same but the numbers get smaller.
A. 6/9
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 2/3 rather than 6/9. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
B. 1/3
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 2/3 rather than 1/3. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
C. 72/108
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 2/3 rather than 72/108. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
D. 2/3
72 and 108 share a greatest common factor of 36. Dividing both by 36 gives 72 ÷36 = 2 and 108 ÷36 = 3. So 72/108 reduces to 2/3. This keeps the value the same while expressing it in simplest terms.
Conclusion
Dividing numerator and denominator by 36 shows the simplest form is 2/3.
Question 20 / 31
Which is the value of 10???
A.
1000
B. 400
C. 100
D. 10000
Rationale
10000 is the value of 10?
A. 1000
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 10000, not 1000. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 400
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 10000, not 400. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 100
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 10000, not 100. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 10000
It aligns with the correct computation for the question and matches the final value 10000. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
Conclusion
Hence, 10000 reflects the appropriate or correct rule without altering the quantities.
Question 21 / 31
How many cubic centimeters (cc) are there in one milliliter (ml)?
A.
0.5
B. 1
C. 2
D. 4
Rationale
1 is the correct answer to the question: How many cubic centimeters (cc) are there in one milliliter (ml)?
In the metric system, milliliters and cubic centimeters measure the same volume. By definition, 1 milliliter is exactly equal to 1 cubic centimeter, so the conversion does not change the numerical value€”only the unit label.
A. 0.5
This does not match the standard metric equivalence. It suggests the volume was incorrectly halved, which is not part of the ml-to-cc conversion.
B. 1
This matches the established metric relationship: 1 ml = 1 cc. No calculation is needed beyond recalling the equivalence.
C. 2
This is too large for a direct conversion. It would imply the volume doubles when switching units, which is incorrect.
D. 4
This greatly overstates the conversion and reflects a misunderstanding of how metric volume units relate.
Conclusion
Since 1 ml and 1 cc represent the same amount of volume, the correct conversion is 1.
Question 22 / 31
What is 18 .34?
A.
540
B. 612
C. 408
D. 646
Rationale
612 is the correct answer to the question: What is 18 .34?
Work the problem by breaking one factor into friendly parts so place value stays clear. Write 34 as 30 + 4. Multiply 18 x 30 first to handle the tens: 18 x 30 = 540. Then multiply 18 x 4 to handle the ones: 18 x 4 = 72. Add the two partial products: 540 + 72 = 612. This method shows exactly where each part of the final answer comes from and reduces the chance of leaving out a piece of the multiplication.
A. 540
540 does not fit the problem once multiplication is completed. This value is only the partial product from 18 x 30 and it ignores the extra 18 x 4 that must be included. A common mistake is stopping after multiplying by the tens place and forgetting to multiply by the ones place. Since 34 is more than 30, the final product must be larger than 540, which confirms 540 cannot be correct.
B. 612
It aligns with the correct computation and matches the final value 612. It reflects multiplying both parts of 34 (30 and 4) by 18 and then combining the results. The product is also reasonable because 18 x 34 should be close to 20 x 34 = 680, and 612 is appropriately smaller.
C. 408
408 does not fit the problem once multiplication is done correctly. This answer commonly appears when the tens place is mishandled, such as treating 34 like 24, or when someone multiplies 12 x 34 instead of 18 x 34. Another common slip is calculating 18 x 20 + 18 x 4 (360 + 72 = 432) and then adjusting incorrectly. Because 18 x 34 must be well above 18 x 30 = 540, 408 is too small to be correct.
D. 646
646 does not fit the problem once the correct multiplication steps are applied. This choice often results from adding partial products incorrectly (for example, mixing 540 with a wrong second product) or making an addition error after distribution. It can also come from rounding and then failing to correct back to an exact product. The correct partial products are 540 and 72, and their sum is 612, not 646.
Conclusion
Breaking 34 into 30 and 4 produces partial products of 540 and 72, and adding them gives 612, so the correct value of 18 .34 is 612.
Question 23 / 31
Which of these numbers is a factor of 42?
A.
21
B. 40
C. 9
D. 24
Rationale
21 is a factor of 42
A factor divides a number evenly, meaning the quotient is a whole number and the remainder is 0. Test 21 by dividing: 42 ÷21 = 2, which is a whole number, so 21 is a factor. You can also confirm using multiplication: 21 x 2 = 42, which shows 21 fits exactly into 42.
A. 21
It aligns with the definition of a factor because 42 ÷21 = 2 with no remainder. It also matches the multiplication fact 21 x 2 = 42, confirming it divides evenly.
B. 40
40 does not fit as a factor because 42 ÷40 is not a whole number. This option may be chosen when someone is thinking of "close numbers" rather than divisibility. Since 40 x 1 = 40 and 40 x 2 = 80, 42 is not a multiple of 40, so 40 cannot be a factor.
C. 9
9 does not fit as a factor because 42 ÷9 is not a whole number. A quick check is to list multiples of 9: 9, 18, 27, 36, 45. Since 42 is not on that list, 9 is not a factor of 42.
D. 24
24 does not fit as a factor because 42 ÷24 is not a whole number. Another way to see this is that 24 x 1 = 24 and 24 x 2 = 48, so 42 falls between them and cannot be a multiple of 24.
Conclusion
Checking divisibility shows 42 ÷21 equals 2 with no remainder, so 21 is a factor of 42.
Question 24 / 31
Which fraction best explains why 4/5 is equivalent to 20/25?
A.
16/20
B. 32/44
C. 0/12
D. 28/42
Rationale
16/20 is the correct answer to the question: Which fraction best explains why 4/5 is equivalent to 20/25?
Equivalent fractions represent the same value even though the numerator and denominator look different. You create an equivalent fraction by multiplying or dividing the numerator and denominator by the same nonzero number. The fraction 20/25 comes from 4/5 by multiplying both numerator and denominator by 5: 4 x 5 = 20 and 5 x 5 = 25. A fraction that "best explains" this idea should also show the same value as 4/5 by using equal scaling. The fraction 16/20 reduces to 4/5 when you divide both by 4, showing it represents the same ratio and reinforcing the equivalence concept.
A. 16/20
It aligns because dividing numerator and denominator by 4 gives 4/5. This shows the same value using a different but proportional pair of numbers, which is exactly what equivalence means.
B. 32/44
32/44 does not fit because it reduces to 8/11, not 4/5. Since the simplified form is different, it cannot explain the equivalence between 4/5 and 20/25.
C. 9/12
9/12 does not fit because it reduces to 3/4. Although it is an equivalent fraction to 3/4, it does not match 4/5, so it does not support the equivalence in the question.
D. 28/42
28/42 does not fit because it reduces to 2/3. This is a different fraction value and cannot explain why 4/5 equals 20/25.
Conclusion
Equivalent fractions come from multiplying or dividing numerator and denominator by the same number. Since 16/20 simplifies to 4/5, it represents the same value and correctly supports why 4/5 is equivalent to 20/25.
Question 25 / 31
What is 3/4 + 1.5?
A.
0.75
B. 2.25
C. 1.75
D. 3
Rationale
2.25 is equal to 3/4 + 1.5?
To add a fraction and a decimal, convert them into the same form. A simple choice is to change 3/4 into a decimal. Divide 3 by 4: 3 ÷4 = 0.75. Now add using aligned decimals: 0.75 + 1.50 = 2.25. This method prevents mixing fraction and decimal parts incorrectly and keeps place value consistent.
A. 0.75
0.75 does not fit because it represents only 3/4 and ignores the additional 1.5. This error often happens when someone converts the fraction correctly but forgets to complete the addition.
B. 2.25
It aligns with the correct computation and matches the sum after converting 3/4 to 0.75 and adding it to 1.5.
C. 1.75
1.75 does not fit the correct sum. This often results from adding 0.75 to 1.0 instead of 1.5, or from dropping the 0.5 during addition. Another common cause is misreading 1.5 as 1.0 or 1.25.
D. 3.0
3.0 does not fit because the correct sum is 2.25. This choice often comes from treating 3/4 as 3, or rounding both numbers up aggressively and not returning to the exact calculation.
Conclusion
Converting 3/4 to 0.75 and adding it to 1.5 yields 2.25, and careful decimal alignment confirms the result is 2.25.
Question 26 / 31
What is the largest of these numbers?
A.
0.0505
B. 0.04
C. 0.12
D. 0.2
Rationale
0.2 is the largest of those numbers.
A. 0.0505
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.2, not 0.0505. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 0.040
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.2, not 0.040. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 0.12
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.2, not 0.12. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 0.2
It aligns with the correct computation for the question and matches the final value 0.2. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
Conclusion
Hence, 0.2 is the largest of all those numbers.
Question 27 / 31
Which of the following represents the quantity fifty two and two hundred and five ten thousandths?
A.
52.025
B. 52.25
C. 52.0205
D. 52.205
Rationale
52.0205 g represents the quantity "fifty-two and two hundred five ten-thousandths" because the decimal places indicate tenths, hundredths, thousandths, and ten-thousandths in order, and the digits must be placed exactly in those positions.
The whole-number part is 52. After the decimal, 0 is in the tenths place, 2 is in the hundredths place, 0 is in the thousandths place, and 5 is in the ten-thousandths place. That makes the decimal portion 0.0205, which is read as two hundred five ten-thousandths. Keeping the zeros is essential because they hold the place value of the 2 and the 5.
A. 52.0250
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 52.0205, not 52.0250. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 52.2500
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 52.0205, not 52.2500. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 52.0205
It aligns with the correct computation for the question and matches the final value 52.0205. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
D. 52.2050
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 52.0205, not 52.2050. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
Matching the words to place value gives a whole number of 52 and a decimal portion of 0.0205, so the correct written form is 52.0205 g.
Question 28 / 31
How many mL are in 0.825 L?
A.
82.5 mL
B. 825 mL
C. 8.25 mL
D. 8250 mL
Rationale
There are 825 mL in 0.825 L.
Liters and milliliters are metric units of volume, and the conversion is fixed: 1 liter equals 1000 milliliters. Converting from liters to milliliters means the number becomes 1000 times larger because you are changing to a smaller unit. Multiply 0.825 by 1000 to convert: 0.825 L x 1000 mL/L = 825 mL. This is the same as moving the decimal three places to the right (0.825 †’ 825). The units also confirm the result: liters cancel out, leaving milliliters.
A. 82.5 mL
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 825 mL, not 82.5 mL. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 825 mL
It aligns with the correct computation for the question and matches the final value 825 mL. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
C. 8.25 mL
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 825 mL, not 8.25 mL. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 8250 mL
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 825 mL, not 8250 mL. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
Using 1 L = 1000 mL and multiplying 0.825 by 1000 gives 825 mL, confirming the correct volume is 825 mL.
Question 29 / 31
Find the value of 1 (1/2) ?2/5
A.
12/5
B. 3/5
C. 3 (3/4)
D. 7 (1/2)
Rationale
3 (3/4) is the correct answer to the question: Find the value of 1 (1/2) ÷2/5.
To divide mixed numbers and fractions correctly, first rewrite everything as fractions and then apply the rule for division of fractions. The mixed number 1 (1/2) must be converted to an improper fraction so the operation can be handled consistently. Since 1 (1/2) equals 3/2, the problem becomes (3/2) ÷(2/5). Dividing by a fraction is the same as multiplying by its reciprocal, so this changes to (3/2) x (5/2). Multiplying across gives (3 x 5) ÷(2 x 2) = 15/4. Finally, convert 15/4 back into a mixed number. Dividing 15 by 4 gives 3 with a remainder of 3, which is written as 3 (3/4).
A. 12/5
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 3 (3/4) rather than 12/5. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
B. 3/5
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 3 (3/4) rather than 3/5. This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
C. 3 3/4
Convert 1 (1/2) to an improper fraction: 1 (1/2) = 3/2. Now divide by 2/5: (3/2) ÷(2/5) = (3/2) x (5/2). Multiply: (3x5)/(2x2) = 15/4. Convert 15/4 to a mixed number: 15 ÷4 = 3 remainder 3, so 3 (3/4). This matches the correct option.
D. 7 1/2
This choice does not match what the question is asking for. When you apply the required method carefully, you land on 3 (3/4) rather than 7 (1/2). This kind of result usually comes from a skipped step, a misread operation, or rounding too early.
Conclusion
Converting the mixed number to an improper fraction and changing division to multiplication by the reciprocal gives 15/4, which simplifies to 3 (3/4), confirming the correct value of the expression.
Question 30 / 31
Find the value of 2.35 L + 0.06 L + 1.2 L.
A.
5.491 L
B. 4.056 L
C. 3.61 L
D. 4.11 L
Rationale
3.61 L is the value of 2.35 L + 0.06 L + 1.2 L.
To add decimals accurately, line up the numbers by place value (tenths, hundredths, thousandths) and keep the unit the same. Write each value with the same number of decimal places: 2.35 L, 0.06 L, and 1.20 L. Add the hundredths first: 0.35 + 0.06 = 0.41. Then combine the whole and tenths portion: 2.35 + 0.06 = 2.41. Finally add 1.20: 2.41 + 1.20 = 3.61. Since all quantities are already in liters, no unit conversion is needed€”only correct decimal alignment.
A. 5.491 L
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 4.056 L, not 5.491 L. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
B. 4.056 L
It aligns with the correct computation for the question and matches the final value 4.056 L. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
C. 3.61 L
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 4.056 L, not 3.61 L. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 4.11 L
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 4.056 L, not 4.11 L. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
Writing 1.2 as 1.20 and adding with decimals aligned gives 2.35 + 0.06 = 2.41, then 2.41 + 1.20 = 3.61, so the total volume is 3.61 L.
Question 31 / 31
Find the product of 14.3 and 0.056 rounded to the nearest one hundredth.
A.
0.81
B. 0.8
C. 0.801
D. 0.8
Rationale
0.80 is the correct answer to the question: Find the product of 14.3 and 0.056 rounded to the nearest one hundredth.
To multiply decimals accurately, multiply the numbers as whole numbers first, then place the decimal based on the total number of decimal places in the original factors.
Treat 14.3 as 143 tenths and 0.056 as 56 thousandths, or simply multiply 14.3 x 56 and then divide by 1000.
Compute the product:
14.3 x 56 = 14.3 x (50 + 6)
= (14.3 x 50) + (14.3 x 6)
= 715 + 85.8
= 800.8
Now account for the three decimal places in 0.056:
14.3 x 0.056 = 800.8 ÷1000 = 0.8008
Round 0.8008 to the nearest one hundredth (two decimal places). The hundredths digit is 0 (in 0.80), and the thousandths digit is 0, so the value stays 0.80.
A. 0.81
It aligns with the correct computation for the question and matches the final value 0.81. It reflects applying the appropriate rule(s) without changing the meaning of the given quantities.
B. 0.80
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.81, not 0.80. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
C. 0.801
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.81, not 0.801. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
D. 0.800
It does not fit the problem once the arithmetic or rule is applied carefully. A full step-by-step calculation leads to 0.81, not 0.800. This answer is commonly produced by a sign error, an incorrect order of operations, or a misplaced decimal.
Conclusion
Multiplying gives an exact product of 0.8008, and rounding this value to the nearest one hundredth results in 0.80.
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