Perform each calculation to the correct number of...

Perform each calculation to the correct number of significant figures.
(a) $(78.4-44.889) \div 0.0087$
(b) $(34.6784 \times 5.38)+445.56$
(c) $\left(78.7 \times 10^{5} \div 88.529\right)+356.99$
(d) $(892 \div 986.7)+5.44$

Key Concepts

Significant Figures

Significant figures are the digits in a number that carry meaningful information about its precision. They include all non-zero digits, any zeros between them, and any trailing zeros when they are specified by a decimal point. Understanding significant figures is essential for accurately representing measurement precision and for ensuring that results of calculations are neither over- nor under-reported in terms of accuracy.

Addition and Subtraction in Significant Figures

When performing addition or subtraction, the result should be rounded to the least number of decimal places present in any of the numbers involved. This rule applies because the uncertainty in the final result is determined by the least precise measurement, and keeping extra decimals would falsely imply greater accuracy.

Multiplication and Division in Significant Figures

For multiplication and division, the final result should be rounded so that it has the same number of significant figures as the factor with the fewest significant figures. This approach ensures that the uncertainty in the product or quotient reflects the precision of the individual measurements used in the calculation.

Rounding Procedures

Rounding is the process of adjusting a number to reflect the proper level of precision. In the context of significant figures, rounding involves determining which digits are trustworthy based on the least precise measurement and then omitting excess digits, while following standard rounding rules to decide whether to round up or down.

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