Calculate to the correct number of significant figures. d. (3.14 × 2.4367) - 2.34

Verified step by step guidance

1. Identify the number of significant figures in each number: 3.14 has 3 significant figures, 2.4367 has 5 significant figures, and 2.34 has 3 significant figures.
2. Perform the multiplication: Multiply 3.14 by 2.4367. The result should be rounded to the least number of significant figures from the numbers being multiplied, which is 3 significant figures.
3. Perform the subtraction: Subtract 2.34 from the result of the multiplication. When subtracting, the result should be rounded to the least number of decimal places from the numbers being subtracted.
4. Round the final result to the correct number of significant figures based on the subtraction step.
5. Ensure the final answer is presented with the correct number of significant figures and decimal places.

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 set of rules that dictates the sequence in which calculations should be performed to ensure accurate results. In chemistry and mathematics, the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is commonly used. Following this order is essential when performing calculations involving multiple operations, such as the one in the question.

Subtraction and Significant Figures

When performing subtraction, the result should be reported with the same number of decimal places as the measurement with the least number of decimal places. This rule ensures that the precision of the result reflects the least precise measurement involved in the calculation. In the given question, this principle will guide how to express the final answer after performing the subtraction.