Carry out the following operations and express the answers with the appropriate number of significant numbers. (a) 14.3505 + 2.65 (b) 952.72 - 73.4201

Verified step by step guidance

1. Identify the number of significant figures in each number: 14.3505 has 6 significant figures, and 2.65 has 3 significant figures.
2. Perform the addition: 14.3505 + 2.65.
3. Determine the decimal place of the least precise number: 2.65 has its last significant figure in the hundredths place.
4. Round the result of the addition to the least precise decimal place, which is the hundredths place.
5. Express the final answer with the appropriate number of significant figures based on the least precise measurement.

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. When performing calculations, the result should reflect the precision of the least precise measurement, ensuring that the final answer is reported with the correct number of significant figures.

Addition of Decimals

When adding decimal numbers, the result should be rounded to the least number of decimal places present in any of the numbers being added. This means that the final answer should maintain the same level of precision as the measurement with the fewest decimal places, ensuring that the result is not misleading in terms of accuracy.

Rounding Rules

Rounding rules dictate how to adjust numbers to reflect the appropriate level of precision. When rounding, if the digit to the right of 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. These rules are essential for ensuring that calculations maintain their integrity and accuracy.