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Chapter 1: Problem 45

What is the number of significant figures in each of the following measured quantities? (a) \(902.5 \mathrm{~kg}\), (b) \(3 \times 10^{-6} \mathrm{~m}\), (c) \(0.0096 \mathrm{~L}\), (d) \(2.94 \times 10^{3} \mathrm{~m}^{2}\) (e) \(92.03 \mathrm{~km}\) (f) \(782.234 \mathrm{~g}\).

Short Answer

Expert verified
The number of significant figures for the given measured quantities is as follows: (a) 902.5 kg: 4 significant figures, (b) \(3 \times 10^{-6}\) m: 1 significant figure, (c) 0.0096 L: 2 significant figures, (d) \(2.94 \times 10^{3}\) m²: 3 significant figures, (e) 92.03 km: 4 significant figures, (f) 782.234 g: 6 significant figures.

Step by step solution

01

(1. Significant figures for 902.5 kg)

The number 902.5 contains no leading or trailing zeros. All nonzero digits are significant and the zero between 9 and 2 is also significant. Therefore, there are 4 significant figures in this quantity.
02

(2. Significant figures for \(3 \times 10^{-6}\) m)

In scientific notation, all digits in the base (3 in this case) are significant. Therefore, the quantity has 1 significant figure.
03

(3. Significant figures for 0.0096 L)

According to the rules, leading zeros are not significant. Therefore, the quantity has 2 significant figures—9 and 6.
04

(4. Significant figures for \(2.94 \times 10^{3}\) m²)

In scientific notation, all digits in the base (2.94 in this case) are significant. Therefore, the quantity has 3 significant figures.
05

(5. Significant figures for 92.03 km)

There are no leading or trailing zeros and the zero between 9 and 2 is significant. Therefore, there are 4 significant figures in this quantity.
06

(6. Significant figures for 782.234 g)

There are no leading or trailing zeros, and all nonzero digits are significant. Therefore, there are 6 significant figures in this quantity.

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