Express the results of the following calculations with the correct number of significant figures. (a) (( 3.41 - 0.23)/5.233) * 0.205

Verified step by step guidance

1. Identify the number of significant figures in each number: 3.41 (3 sig figs), 0.23 (2 sig figs), 5.233 (4 sig figs), and 0.205 (3 sig figs).
2. Perform the subtraction: 3.41 - 0.23. The result should have the same number of decimal places as the number with the fewest decimal places (0.23 has 2 decimal places).
3. Divide the result of the subtraction by 5.233. The result should have the same number of significant figures as the number with the fewest significant figures in the division (the result of the subtraction).
4. Multiply the result of the division by 0.205. The result should have the same number of significant figures as the number with the fewest significant figures in the multiplication (0.205 has 3 sig figs).
5. Express the final result with the correct number of significant figures based on 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.

Order of Operations

The order of operations is a mathematical rule that dictates the sequence in which calculations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying this correctly is essential when performing calculations involving multiple operations, as it affects the final result.

Dimensional Analysis

Dimensional analysis is a method used to convert units and ensure that equations are dimensionally consistent. It involves using conversion factors to relate different units and can help in verifying the correctness of calculations. In the context of significant figures, it aids in maintaining the appropriate precision throughout the calculation process.