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

Verified step by step guidance

1. Identify the number of significant figures in each number: 3.7 has 2 significant figures and 94.61 has 4 significant figures.
2. When dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.
3. Since 3.7 has the fewest significant figures (2), the result of the division should also have 2 significant figures.
4. Perform the division: 3.7 divided by 94.61.
5. Round the result to 2 significant figures to express the final answer.

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 used.

Rules for Division in Significant Figures

When performing division, the result should be expressed 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 is not overstated and reflects the limitations of the least precise measurement involved in the calculation.

Calculating with Significant Figures

To calculate with significant figures, one must first identify the number of significant figures in each value involved in the operation. After performing the calculation, the result must be rounded to match the significant figures of the least precise measurement. This process is essential for maintaining accuracy and reliability in scientific calculations.