Express the results of the following calculations with the correct number of significant figures. (b) ( 5.556 * 2.3)/(4.223 - 0.08)

Verified step by step guidance

1. Identify the number of significant figures in each number: 5.556 has 4 significant figures, 2.3 has 2 significant figures, 4.223 has 4 significant figures, and 0.08 has 1 significant figure.
2. Perform the multiplication: Multiply 5.556 by 2.3. The result should be expressed with the same number of significant figures as the number with the fewest significant figures, which is 2.3 with 2 significant figures.
3. Perform the subtraction: Subtract 0.08 from 4.223. The result should be expressed with the same number of decimal places as the number with the fewest decimal places, which is 0.08 with 2 decimal places.
4. Divide the result of the multiplication by the result of the subtraction. The final result should be expressed with the same number of significant figures as the number with the fewest significant figures from the previous steps.
5. Ensure the final answer is rounded to the correct number of significant figures based on the division result.

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 be expressed with the same number of significant figures as the measurement with the least number of significant figures involved in the calculation.

Order of Operations

Order of operations is a set of rules 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. In the given calculation, operations within parentheses should be completed first, followed by multiplication and division.

Calculating with Significant Figures

When performing calculations, the rules for significant figures differ for multiplication/division and addition/subtraction. For multiplication and division, the final result should have the same number of significant figures as the measurement with the fewest significant figures. For addition and subtraction, the result should be rounded to the least precise decimal place. This ensures that the precision of the result reflects the precision of the measurements used.