Calculate to the correct number of significant figures. a. 0.004 + 0.09879 b. 1239.3 + 9.73 + 3.42 c. 2.4 - 1.777 d. 532 + 7.3 - 48.523

검증된 단계별 안내

Identify the number of significant figures in each number involved in the calculations.

For addition and subtraction, the result should be reported with the same number of decimal places as the number with the fewest decimal places.

a. Add 0.004 and 0.09879. The number with the fewest decimal places is 0.004, which has 3 decimal places.

b. Add 1239.3, 9.73, and 3.42. The number with the fewest decimal places is 1239.3, which has 1 decimal place.

c. Subtract 1.777 from 2.4. The number with the fewest decimal places is 2.4, which has 1 decimal place.

d. Subtract 48.523 from the sum of 532 and 7.3. The number with the fewest decimal places is 532, which has 0 decimal places.

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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.

Rules for Addition and Subtraction

When performing addition or subtraction, the result should be reported with the same number of decimal places as the measurement with the least number of decimal places. This rule ensures that the precision of the result is not overstated, maintaining the integrity of the data derived from the least precise measurement.

Rules for Multiplication and Division

In multiplication and division, the result should have the same number of significant figures as the measurement with the least number of significant figures. This rule is important for maintaining the accuracy of calculations, as it prevents the misleading representation of precision in the final result.