Express the results of the following calculations with the correct number of significant figures. (b) 94.61 / 3.7

Verified step by step guidance

1. Identify the number of significant figures in each number: 94.61 has four significant figures, and 3.7 has two significant figures.
2. When dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
3. Perform the division: 94.61 divided by 3.7.
4. Round the result to two significant figures, as 3.7 has the fewest significant figures.
5. Express the final result with the correct number of significant figures.

Key Concepts

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 Division in Significant Figures

When performing division, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures. This rule ensures that the precision of the result does not exceed that of the least precise measurement, maintaining the integrity of the data.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. If the digit following the last significant figure is less than 5, the last significant figure remains unchanged; if it is 5 or greater, the last significant figure is increased by one. Proper rounding is essential for ensuring that calculations are both accurate and appropriately precise.