Perform the following calculations with the correct number of significant figures. (c) 7.662 - 7.425

Verified step by step guidance

1. Identify the number of decimal places in each number. The first number, 7.662, has three decimal places, and the second number, 7.425, also has three decimal places.
2. Subtract the numbers using standard subtraction rules: 7.662 - 7.425.
3. Calculate the result of the subtraction.
4. Determine the number of significant figures in the result based on the original numbers. Since both original numbers have three decimal places, the result should also be rounded to three decimal places.
5. Round the result, if necessary, to ensure it has 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 ensuring that calculations reflect the precision of the measured values.

Subtraction and Significant Figures

When performing subtraction, the result should be reported with the same number of decimal places as the measurement with the least number of decimal places. This rule ensures that the precision of the result is not overstated, maintaining the integrity of the data derived from the calculations.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. When 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. Proper rounding is essential for maintaining accuracy in calculations involving significant figures.