Final answer:
Calculations must consider the rules of significant figures: the result matches the least precise measurement when adding or subtracting, and the least number of significant figures when multiplying or dividing. For example, 4.7 - 2.65 equals 2.05 following these rules.
Step-by-step explanation:
To perform these calculations, we need to be mindful of the rules for significant digits:
- When adding or subtracting, the result should have the same number of decimal places as the number with the least decimal places.
- When multiplying or dividing, the result should have the same number of significant figures as the number with the least number of significant figures.
Examples of calculations with proper number of significant figures are:
- 4.7 (two significant figures) - 2.65 (three significant figures) = 2.05 when rounded to two decimal places to match the less precise measurement (4.7).
- 5.20 (three significant figures) + 4.80 (three significant figures) = 10.00 when rounded to two decimal places to match the more precise measurement (5.20).
Here are more examples based on the provided calculations:
- 56.0 (three significant figures) + 3.44 (three significant figures) = 59.4 (should be expressed to one decimal place).
- 0.00665 (three significant figures) + 1.004 (four significant figures) = 1.011 (should be expressed with three decimal places to match the less precise measurement, 0.00665).
- 45.99 (four significant figures) - 32.8 (three significant figures) = 13.2 (should be expressed to one decimal place since 32.8 has one decimal place).
For multiplication:
- 62.8 (three significant figures) x 34 (two significant figures) = 2100 (or 2.13 x 103) when rounded to two significant figures.
And for a combination of operations:
- 421.23 g divided by 486 mL (three significant figures) results in a quotient with three significant figures (since 486 has three significant figures).