Lesson 18: Calculating with Units of Measure

New Concept

You can use unit conversion factors to change one unit of measure to another.

What’s next

Next, you'll practice selecting the correct conversion factor to change units for length, area, and rates of speed.

A conversion factor is a fraction equal to 1, such as

To change 720 inches to feet:

Think of conversion factors as magical translators for units. You're not changing a measurement's value, just its language! By multiplying by the right fraction, you make 'inches' disappear and 'feet' appear in their place. It's all about setting up the fraction so the unwanted units are on opposite sides and cancel each other out.

Significant digits indicate the precision of a measurement. Rules for counting them are: 1. Nonzero digits are significant. 2. Zeros between significant digits are significant. 3. Leading zeros are not significant. 4. Zeros after the last nonzero digit and to the right of a decimal point are significant.

The number $405.08$ has 5 significant digits. The number $0.0075$ has 2 significant digits. The number $0.09100$ has 4 significant digits, as the trailing zeros after the decimal are counted.

Significant digits are the 'trustworthy' numbers in a measurement. They tell you how precise that measurement really is. Think of leading zeros as just placeholders, like the empty space before a sentence begins. But those trailing zeros after a decimal? They're super important—they prove you measured carefully right down to that tiny fraction!

When adding or subtracting, the answer should have the same number of decimal places as the measurement with the fewest decimal places. When multiplying or dividing, the answer should have the same number of significant digits as the measurement with the fewest significant digits. This ensures the result isn't more precise than the least precise measurement.

Addition: $5.21 \text{ mi} + 4.782 \text{ mi} + 0.3 \text{ mi} = 10.292 \text{ mi}$, which rounds to $10.3 \text{ mi}$. Multiplication: $3.09 \text{ ft} \times 0.060 \text{ ft} \times 205 \text{ ft} = 38.007 \text{ ft}^3$, which rounds to $38 \text{ ft}^3$.

A calculation is only as reliable as its weakest link! For addition and subtraction, your answer can't be more detailed than your least detailed number. For multiplication and division, you are limited by the measurement with the fewest 'trustworthy' digits. Don't claim your answer is super-precise if one of your starting numbers was just a rough estimate.