Perform the following mathematical operation and report the answer to the correct number of significant figures.
$7.9256 \div 4.372=[?]$
Answer (1)
Divide 7.9256 by 4.372 to get 1.8128087831655995.
Determine the number of significant figures in each number: 7.9256 has 5, and 4.372 has 4.
Round the result to the smallest number of significant figures, which is 4.
The final answer, rounded to 4 significant figures, is 1.813 .
Explanation
Understanding the Problem We are asked to perform the division 7.92564.372 and report the answer to the correct number of significant figures.
Performing the Division First, we perform the division: 7.92564.372 = 1.8128087831655995
Determining Significant Figures Next, we need to consider significant figures. The number 7.9256 has 5 significant figures, and the number 4.372 has 4 significant figures. When dividing, the result should be rounded to the smallest number of significant figures in the numbers being divided. In this case, that is 4 significant figures.
Rounding to Correct Significant Figures Rounding 1.8128087831655995 to 4 significant figures gives 1.813 .
Final Answer Therefore, the final answer is 1.813 .
Examples
When calculating the density of an object by dividing its mass by its volume, it's crucial to report the result with the correct number of significant figures. For example, if an object has a mass of 7.9256 grams and a volume of 4.372 cubic centimeters, dividing these values gives the density. Reporting the density as 1.813 g/cm³ (with 4 significant figures) accurately reflects the precision of the measurements used.
