An electron has a mass of 9.11×10^−31 kg. When this value is represented in standard notation, how many zeros are between the decimal point and the nearest non-zero digit?
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A
29
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B
30
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C
31
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D
32
There are 30 zeros between the decimal point and the nearest non-zero digit.
Converting from scientific notation (a × 10⁻ⁿ) to standard notation for a number less than one involves moving the decimal point *n* places to the left. The number of leading zeros in the resulting decimal is *n - 1*, because the first non-zero digit from the coefficient (a) occupies the *n*th place to the right of the decimal.
A) 29
This count would correspond to a scientific notation exponent of -30. With an exponent of -31, moving the decimal point 30 places would leave the first digit in the 30th place, resulting in 29 leading zeros. However, the given exponent is -31, requiring one more decimal place move.
B) 30
The coefficient is 9.11 and the exponent is -31. To write this in standard notation, the decimal point in 9.11 is moved 31 places to the left: 0.000000000000000000000000000000911 kg. The first non-zero digit (9) is in the 31st decimal place. The digits between the decimal point and this '9' are zeros occupying the 1st through 30th decimal places. Therefore, there are 30 zeros.
C) 31
This number represents the total number of decimal places moved, which includes the place finally occupied by the first non-zero digit (the 31st place). The question specifically asks for the number of zeros between the decimal point and that digit, which is one less than the exponent's absolute value.
D) 32
A count of 32 leading zeros would imply an original exponent of -33 or similar, which has no basis in the given value of 9.11 × 10⁻³¹.
Conclusion:
For a number expressed in proper scientific notation as N × 10⁻ⁿ, where N is between 1 and 10, the conversion to standard decimal notation yields a number with (*n* - 1) zeros between the decimal point and the first significant digit of N. Applying this rule to the electron mass, 9.11 × 10⁻³¹, with *n* = 31, results in 30 leading zeros.
Topic Flashcards
Click to FlipConvert the number 6.02 × 10 − 23 6.02×10 −23 to standard notation. How many zeros are between the decimal point and the first non-zero digit?
0.0000000000000000000000602 0.0000000000000000000000602; there are 22 zeros.
If a number is written in scientific notation as N × 10 − n N×10 −n , where 1 ≤ N < 10 1≤N<10, what is the formula for the number of zeros between the decimal point and the first digit of N N in standard form?
There are n − 1 n−1 zeros.
Write the electron mass 9.11 × 10 − 31 kg 9.11×10 −31 kg in standard decimal notation.
0.000000000000000000000000000000911 kg (30 zeros after the decimal before the 9).
Convert 4.5 × 10 − 7 4.5×10 −7 to standard notation and count the zeros between the decimal and the first non-zero digit.
0.00000045; there are 6 zeros.
The number 1.0 × 10 − 12 1.0×10 −12 in standard notation is often used as a prefix (pico). Write it out and state how many zeros follow the decimal before the 1.
0.000000000001 0.000000000001; there are 11 zeros.