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Question

# Perform each of the following calculations, and give an answer with the correct number of significant figures: a. $45.7 \times 0.034$ b. $0.00278 \times 5$ c. $\frac{34.56}{1.25}$ d. $\frac{(0.2465)(25)}{1.78}$ e. $\left(2.8 \times 10^4\right)\left(5.05 \times 10^{-6}\right)$ f. $\frac{\left(3.45 \times 10^{-2}\right)\left(1.8 \times 10^5\right)}{\left(8 \times 10^3\right)}$

Solution

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Since the measurements are never infinitely accurate, some value must be estimated. To determine significant figures, we follow the following rules:

1. All zeros at the beginning of the result are ignored

2. All zeros after a number are ignored unless they come after a decimal point when counted as significant figures

3. All other digits, including the zero between the two numbers, are considered significant figures

The number of significant figures of the result must be equal to the number of significant figures of a given value that has less significant figures.

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