Learning Outcomes
- Convert between the U.S. customary units and metric units of length, weight/mass, and volume
Conversions between U.S. and Metric Measurement Systems
Many measurements in the United States are made in metric units. A drink may come in [latex]\text{2-liter}[/latex] bottles, calcium may come in [latex]\text{500-mg}[/latex] capsules, and we may run a [latex]\text{5-K}[/latex] race. To work easily in both systems, we need to be able to convert between the two systems.
The reference table below shows some of the most common conversions.
| Conversion Factors Between U.S. and Metric Systems | ||
|---|---|---|
| Length | Weight | Volume |
| [latex]1[/latex] in = [latex]2.54[/latex] cm
[latex]1[/latex] ft = [latex]0.305[/latex] m [latex]1[/latex] yd = [latex]0.914[/latex] m [latex]1[/latex] mi = [latex]1.61[/latex] km [latex]1[/latex] m = [latex]3.28[/latex] ft |
[latex]1[/latex] lb = [latex]0.45[/latex] kg
[latex]1[/latex] oz = [latex]28[/latex] g [latex]1[/latex] kg = [latex]2.2[/latex] lb |
[latex]1[/latex] qt = [latex]0.95[/latex] L
[latex]1[/latex] fl oz = [latex]30[/latex] mL [latex]1[/latex] L = [latex]1.06[/latex] qt |
We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors.
example
Lee’s water bottle holds [latex]500[/latex] mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce.
Solution
| [latex]500[/latex] mL | |
| Multiply by a unit conversion factor relating mL and ounces. | [latex]500\text{mL}\cdot\Large\frac{1\text{fl oz}}{30\text{mL}}[/latex] |
| Simplify. | [latex]\Large\frac{500\text{fl oz}}{30}[/latex] |
| Divide. | [latex]16.7\text{fl. oz.}[/latex] |
| The water bottle holds [latex]16.7[/latex] fluid ounces. |
Try It
Example
A bottle contains 1.5 liters of a beverage. How many 250 mL servings can be made from that bottle?
The conversion factors in the reference table are not exact, but the approximations they give are close enough for everyday purposes. In the last example, we rounded the number of fluid ounces to the nearest tenth.
Exercises
Soleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in [latex]100[/latex] kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.
TRY IT
Understanding the context of real-life application problems is important. Look for words within the problem that help you identify what operations are needed, and then apply the correct unit conversions. Checking your final answer by using another conversion method (such as the ‘move the decimal’ method, if you have used dimensional analysis to solve the problem) can cut down on errors in your calculations.
Summary
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. Units in the metric system are all related by a power of 10, which means that each successive unit is 10 times larger than the previous one.
This makes converting one metric measurement to another a straightforward process, and is often as simple as moving a decimal point. It is always important, though, to consider the direction of the conversion. If you are converting a smaller unit to a larger unit, then the decimal point has to move to the left (making your number smaller); if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right (making your number larger).
Dimensional analysis can also be applied to conversions within the metric system. To use dimensional analysis, you multiply the original measurement by unit fractions; this allows you to represent the original measurement in a different measurement unit.
