Which statement regarding significant figures is false?

A. Zeros can be significant.

B. When multiplying, the answer is determined by the number of significant figures.

C. When adding, the answer is determined by the number of decimal places.

D. When dividing, the answer is determined by the number of decimal places.

E. The number 50,004 has five significant figures.

D is incorrect. When dividing, the answer is determined by the number of significant figures.

Answered by Kyllie | 2024-06-10

The question involves understanding significant figures and their rules, particularly concerning operations and when zeros are considered significant. To address the student's question, let's analyze each statement:

Zeros can be significant: This is true. Zeros are significant except when they only serve as placekeepers. For example, in 10.053, the zeros are significant because they are between nonzero digits, making a total of five significant figures.
When multiplying, the answer is determined by the number of significant figures: This is true. When multiplying or dividing, the number of significant figures in the result should match the factor with the least number of significant figures.
When adding, the answer is determined by the number of decimal places: This is true. The precision of the sum (or difference) in an addition (or subtraction) operation is determined by the least number of decimal places, not significant figures.
When dividing, the answer is determined by the number of decimal places: This is false. Similar to multiplication, the precision of the quotient in a division operation is determined by the original number with the least number of significant figures.
The number 50,004 has five significant figures: This is true. All nonzero digits are significant, and zeros between nonzero digits are also significant.

So, the false statement is (d): When dividing, the answer is determined by the number of decimal places .

Answered by ArmyArcherd | 2024-06-24

The false statement is D, which claims that when dividing, the answer's precision is based on decimal places. In reality, for division, the number of significant figures in the answer is determined by the quantity with the least significant figures. All other statements regarding significant figures are true.
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Answered by ArmyArcherd | 2024-12-23