Express the results of the following calculations with the correct number of significant figures. (a) 4.884 * 2.05

Verified step by step guidance

1. Identify the number of significant figures in each number: 4.884 has 4 significant figures, and 2.05 has 3 significant figures.
2. Perform the multiplication: 4.884 \times 2.05.
3. Determine the number of significant figures for the final result: The result should have the same number of significant figures as the number with the fewest significant figures used in the calculation, which is 3.
4. Round the result of the multiplication to 3 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 scientific contexts.

Multiplication and Significant Figures

When multiplying numbers, the result should be expressed with the same number of significant figures as the factor with the least significant figures. This rule ensures that the precision of the result reflects the least precise measurement involved in the calculation, maintaining the integrity of the data.

Rounding Rules

Rounding rules dictate how to adjust numbers to the correct number of significant figures. If the digit to be dropped is less than 5, the last retained digit remains unchanged; if it is 5 or greater, the last retained digit is increased by one. Proper rounding is essential to ensure that the final answer is both accurate and appropriately precise.