Carry out the following multiplications and divisions,...

Carry out the following multiplications and divisions, expressing your answer to the correct number of significant figures. Assume that all numbers are measured numbers. a. $2.000 \times 0.200 \times 0.20$ b. $3.6750 \times 0.04503$ c. $0.0030 \times 0.400 \times 4.00$ d. $\frac{6.0000}{33.00}$ e. $\frac{45,000}{1.2345}$ f. $\frac{3.00 \times 6.53}{13.567}$

Carry out the following multiplications and divisions, expressing your answer to the correct number of significant figures. Assume that all numbers are measured numbers.
a. $2.000 \times 0.200 \times 0.20$
b. $3.6750 \times 0.04503$
c. $0.0030 \times 0.400 \times 4.00$
d. $\frac{6.0000}{33.00}$
e. $\frac{45,000}{1.2345}$
f. $\frac{3.00 \times 6.53}{13.567}$

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Key Concepts

Rounding

Rounding is the process of reducing the number of digits in a number while attempting to keep its value similar, following specific rules. In the context of significant figures, rounding entails adjusting the final result so that it contains only the allowed number of significant figures, without introducing additional precision that was not present in the original measurements.

Significant Figures

Significant figures refer to the digits in a number that contribute to its precision. These include all non-zero digits, any zeros between significant digits, and, in the case of measured numbers, trailing zeros when a decimal point is present. When performing calculations, the number of significant figures in the result should reflect the precision of the least precise measurement used in the calculation.

Multiplication and Division with Significant Figures

In operations involving multiplication or division, the final answer must be rounded to the same number of significant figures as the measurement with the fewest significant figures. This rule ensures that the result does not imply a greater precision than the least precise measured number.

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