How many significant figures are in the following numbers? (a) 100.0 \pm 0.3 (b) 5.000 \times 10^{14} (c) 4.20 \times 10^{-4} (d) 0.0090
The Correct Answer and Explanation is:
Let’s analyze each number:
(a) 100.0 ± 0.3
This number, 100.0, is written with a decimal point at the end. Any number with a decimal point is significant. The number “100.0” has 4 significant figures: the “1,” the two zeros, and the decimal point.
The uncertainty value, ± 0.3, does not affect the count of significant figures in the measured value itself. The uncertainty simply indicates the precision of the measurement, but it doesn’t change the significant figures of the number.
Answer: 4 significant figures.
(b) 5.000 × 10¹⁴
This number is expressed in scientific notation. In scientific notation, all digits written in the mantissa (the part before the × 10ⁿ) are significant. Here, “5.000” has 4 digits—”5,” the three zeros, and the decimal point.
The exponent 101410^{14}1014 tells you the scale of the number, but it doesn’t affect the number of significant figures.
Answer: 4 significant figures.
(c) 4.20 × 10⁻⁴
In scientific notation, the number 4.20 has a decimal point, and the digits “4,” “2,” and the zero are all significant. The zero is significant because it is after the decimal point and indicates precision.
Thus, the number “4.20” has 3 significant figures.
Answer: 3 significant figures.
(d) 0.0090
The leading zeros in this number (0.00) are not significant. They are just placeholders indicating the position of the decimal point. However, the “9” and the trailing zero after the decimal point are significant. The zero is significant because it is after the decimal point and indicates the precision of the measurement.
Thus, “0.0090” has 2 significant figures.
Answer: 2 significant figures.
Summary of Answers:
- (a) 100.0 ± 0.3 → 4 significant figures
- (b) 5.000 × 10¹⁴ → 4 significant figures
- (c) 4.20 × 10⁻⁴ → 3 significant figures
- (d) 0.0090 → 2 significant figures
The key takeaway is that significant figures are influenced by the presence of a decimal point, the presence of trailing zeros, and whether the number is in scientific notation.
