Calculate to the correct number of significant figures. a. 89.3 × 77.0 × 0.08

검증된 단계별 안내

Identify the number of significant figures in each number: 89.3 has 3 significant figures, 77.0 has 3 significant figures, and 0.08 has 1 significant figure.

When multiplying numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

In this case, the number with the fewest significant figures is 0.08, which has 1 significant figure.

Perform the multiplication: 89.3 * 77.0 * 0.08.

Round the result to 1 significant figure, as determined by the number with the fewest significant figures.

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주요 개념

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Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in chemistry, as it reflects the precision of the data used.

Multiplication and Significant Figures

When multiplying numbers, the result should be reported with the same number of significant figures as the factor with the least significant figures. This rule ensures that the precision of the result is not overstated. For example, in the calculation of 89.3 * 77.0 * 0.08, the number of significant figures in each factor must be considered to determine the final answer's precision.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. If the digit to be dropped is less than 5, the last retained digit remains unchanged; if it is 5 or greater, the last retained digit is increased by one. Proper rounding is essential in calculations to maintain the integrity of significant figures and ensure accurate results.