Carry out the following operations and express the answers with the appropriate number of significant numbers. (a) 16.234 + 8.722 × 0.6746

Verified step by step guidance

1. insert step 1> Start by identifying the order of operations, which follows the BODMAS/BIDMAS rule: Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction. In this problem, multiplication should be performed before addition.
2. insert step 2> Perform the multiplication: Calculate \(8.722 \times 0.6746\).
3. insert step 3> Determine the number of significant figures for the multiplication result. The number with the least significant figures in the multiplication is 0.6746, which has 4 significant figures. Therefore, the result of the multiplication should be expressed with 4 significant figures.
4. insert step 4> Perform the addition: Add the result from the multiplication to 16.234.
5. insert step 5> Determine the number of decimal places for the final result. In addition, the result should have the same number of decimal places as the number with the least decimal places. Here, 16.234 has 3 decimal places, so the final result should be expressed with 3 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. 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 to ensure accuracy.

Order of Operations

The 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 expression, multiplication must be performed before addition.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division, which are fundamental to solving mathematical expressions. Each operation has specific rules regarding how to handle significant figures and rounding. Understanding how to correctly apply these operations is essential for obtaining accurate results in calculations.