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

검증된 단계별 안내

Identify the number of significant figures in each number: 0.004 has 1 significant figure, and 0.09879 has 5 significant figures.

When adding or subtracting, the result should be reported with the same number of decimal places as the number with the fewest decimal places.

0.004 has 3 decimal places, and 0.09879 has 5 decimal places.

Perform the addition: 0.004 + 0.09879.

Round the result to 3 decimal places, as 0.004 has the fewest decimal places.

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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.

Addition and Significant Figures

When performing addition, 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 reflects the least precise measurement involved in the calculation.

Rounding Rules

Rounding rules dictate how to adjust numbers to maintain significant figures. When rounding, if the digit to be dropped is less than five, the last retained digit remains unchanged; if it is five or greater, the last retained digit is increased by one. This process is essential for ensuring that the final answer is expressed with the correct level of precision.