Calculate to the correct number of significant figures. a. 97.530 * 4.020 / 100.04

Verified step by step guidance

1. Identify the number of significant figures in each number: 97.530 has 5 significant figures, 4.020 has 4 significant figures, and 100.04 has 5 significant figures.
2. Perform the multiplication first: Multiply 97.530 by 4.020.
3. Determine the number of significant figures for the result of the multiplication: The result should have the same number of significant figures as the number with the fewest significant figures in the multiplication, which is 4 (from 4.020).
4. Perform the division: Divide the result of the multiplication by 100.04.
5. Determine the number of significant figures for the final result: The final result should have the same number of significant figures as the number with the fewest significant figures in the entire calculation, which is 4 (from the multiplication step).

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.

Multiplication and Division Rules for Significant Figures

When performing multiplication or division, the result should be reported 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 least precise measurement involved in the calculation.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which calculations should be performed to ensure accurate results. In chemistry calculations, it is essential to follow these rules—parentheses first, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction—to avoid errors in the final answer.