Question

The correct number of significant figures in the number 4.0 × 10⁻² is:

1) 1
2) 2
3) 3
4) ambiguous
5) none of the above

Answer 1

The number 4.0 × 10⁻² has 2 significant figures, since the zero after the decimal in '4.0' is significant.

Step-by-step explanation:

The correct number of significant figures in the number 4.0 × 10⁻² is 2. When a number is written in scientific notation, all the digits in the coefficient are considered significant. In this case, '4.0' consists of two significant figures—the '4', which is a non-zero digit, and the '0', which is significant because it comes after a non-zero digit and is to the right of the decimal point.

This is unlike the integer '1400', which is ambiguous because we cannot tell if the trailing zeros are measured or just place-holding. Therefore, '1.4 x 10³' has two significant figures and '1.40 × 10³' has three significant figures, because the zeros after the decimal are measured and significant.