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

Verified step by step guidance

1. Identify the number of significant figures in each value. For 7.662, there are 4 significant figures, and for 7.425, there are also 4 significant figures.
2. When performing subtraction, the result should be rounded to the least precise decimal place of the numbers involved. In this case, both numbers have their least precise decimal place in the thousandths place (three decimal places).
3. Perform the subtraction operation symbolically: $7.662-7.425$.
4. Determine the result of the subtraction and ensure it is rounded to the thousandths place, as determined in step 2.
5. Express the final result with the correct number of significant figures, ensuring it matches the precision of the least precise decimal place.

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. Typically, 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. Proper rounding is essential for maintaining accuracy in calculations involving significant figures.