Step-by-Step Guidance: Evaluating a Multi-Step Arithmetic Expression with Significant Figures

Q: Evaluate the following expression, paying attention to significant figures:

$(0.523)(1.2161 - 0.99) + \left(\frac{2.648}{0.87}\right)(84 - 81.98)$

Background

Topic: Significant Figures in Arithmetic Calculations

This question tests your ability to perform multi-step arithmetic operations (addition, subtraction, multiplication, division) while correctly applying the rules for significant figures at each step.

Key Terms and Formulas

• Significant Figures: The number of meaningful digits in a value.

• Rules for Significant Figures:

  • For addition/subtraction: The result should have the same number of decimal places as the value with the fewest decimal places.

  • For multiplication/division: The result should have the same number of significant figures as the value with the fewest significant figures.

Step-by-Step Guidance

1. Start with the operations inside the parentheses:

   • Calculate $1.2161 - 0.99$. Remember to apply the rule for significant figures in subtraction (match the least number of decimal places).

   • Calculate $84 - 81.98$. Again, apply the rule for decimal places.

2. Multiply and divide as indicated:

   • Multiply the result from step 1a by $0.523$. Use the multiplication rule for significant figures.

   • Divide $2.648$ by $0.87$. Apply the division rule for significant figures.

3. Multiply the result of the division by the result from step 1b:

   • This gives you the value for the second term in the sum.

4. Add the two terms together:

   • When adding, match the result to the least number of decimal places from the two terms.

Try solving on your own before revealing the answer!