Significant Figures and Scientific Notation in Physics Calculations

Q1. Significant Figures: If you multiply 6.022 × 1023 by 2, which of the following is the correct way to express the answer with the proper number of significant figures?

Background

Topic: Significant Figures and Scientific Notation

This question tests your understanding of how to properly express the result of a multiplication operation in scientific notation, while respecting the rules for significant figures. This is a foundational skill in Physics with Calculus, as it ensures that calculations reflect the precision of the measured values.

Key Terms and Formulas:

• Significant Figures: The digits in a number that are reliable and necessary to indicate its precision.

• Scientific Notation: A way of expressing very large or very small numbers using powers of ten.

• Multiplication Rule: When multiplying numbers, the result should have the same number of significant figures as the factor with the fewest significant figures.

Step-by-Step Guidance

1. Identify the number of significant figures in each factor. $6.022 \times 10^{23}$ has four significant figures, while $2$ (if written as just '2') has one significant figure.

2. Recall the multiplication rule for significant figures: the answer should have the same number of significant figures as the factor with the fewest significant figures.

3. Multiply the numbers: $6.022 \times 10^{23} \times 2$.

4. Express the result in scientific notation, rounding to the correct number of significant figures.

5. Set up the answer so that it matches the significant figure rule, but do not perform the final rounding or selection yet.

Try solving on your own before revealing the answer!

Final Answer: 1 × 1024

The answer should be expressed with one significant figure, since '2' has only one. The correct scientific notation is $1 \times 10^{24}$.

This reflects the proper use of significant figures in multiplication: the result cannot be more precise than the least precise factor.