Calculate to the correct number of significant figures. c. 4.005 × 74 × 0.007

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Identify the number of significant figures in each number: 4.005 has 4 significant figures, 74 has 2 significant figures, and 0.007 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.

Multiply the numbers: 4.005 \(\times\) 74 \(\times\) 0.007.

Determine the number of significant figures for the final result based on the number with the fewest significant figures, which is 1 in this case.

Round the calculated result to 1 significant figure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, if one number has three significant figures and another has two, the final answer should be rounded to two significant figures.

Rounding Rules

Rounding rules dictate how to adjust numbers to the correct number of significant figures. 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. Mastering these rules is essential for ensuring that calculations maintain the appropriate level of precision.

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