Metric System Basics
Learning Outcomes
- Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume
- Define the metric prefixes and use them to perform basic conversions among metric units
- Solve application problems using metric units
- State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.
- Convert from one temperature scale to the other, using conversion formulas
What Is Metric?
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the word meter is part of all of these units. The metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a bit later. For now, notice how this idea of getting bigger or smaller by 10 is very different than the relationship between units in the U.S. customary system, where 3 feet equals 1 yard, and 16 ounces equals 1 pound.Length, Mass, and Volume
The table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.Length | Mass | Volume |
basic units | ||
meter | gram | liter |
other units you may see | ||
kilometer | kilogram | dekaliter |
centimeter | centigram | centiliter |
millimeter | milligram | milliliter |
The handle of a shovel is about 1 meter. | A paperclip weighs about 1 gram. | A medium-sized container of milk is about 1 liter. |
Common Measurements in Customary and Metric Systems | |
Length | 1 centimeter is a little less than half an inch. |
1.6 kilometers is about 1 mile. | |
1 meter is about 3 inches longer than 1 yard. | |
Mass | 1 kilogram is a little more than 2 pounds. |
28 grams is about the same as 1 ounce. | |
Volume | 1 liter is a little more than 1 quart. |
4 liters is a little more than 1 gallon. |
Prefixes in the Metric System
The metric system is a base 10 system. This means that each successive unit is 10 times larger than the previous one. The names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, you look at the base.Prefixes in the Metric System | ||||||
kilo- | hecto- | deka- | meter gram liter | deci- | centi- | milli- |
1,000 times larger than base unit | 100 times larger than base unit | 10 times larger than base unit | base units | 10 times smaller than base unit | 100 times smaller than base unit | 1,000 times smaller than base unit |
- A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).
- A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).
- A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).
Measuring Mass in the Metric System | ||||||
kilogram (kg) | hectogram (hg) | dekagram (dag) | gram (g) | decigram (dg) | centigram (cg) | milligram (mg) |
1,000 grams | 100 grams | 10 grams | gram | 0.1 gram | 0.01 gram | 0.001 gram |
Try It
Which of the following sets of three units are all metric measurements of length? A) inch, foot, yard B) kilometer, centimeter, millimeter C) kilogram, gram, centigram D) kilometer, foot, decimeterAnswer: B) kilometer, centimeter, millimeter All of these measurements are from the metric system. You can tell they are measurements of length because they all contain the word meter.
Example
Convert 1 centimeter to kilometers.Answer: Identify locations of kilometers and centimeters.
km | hm | dam | m | dm | cm | mm |
^ | ^ |
[latex]\div10[/latex] | [latex]\div10[/latex] | [latex]\div10[/latex] | [latex]\div10[/latex] | [latex]\div10[/latex] | ||
km | hm | dam | m | dm | cm | mm |
^ | [latex]\leftarrow[/latex] | [latex]\leftarrow[/latex] | [latex]\leftarrow[/latex] | [latex]\leftarrow[/latex] | ^ |
[latex]1\text{ cm}\div10\div10\div10\div10\div10=0.00001\text{ km}[/latex]
1 centimeter (cm) = 0.00001 kilometers (km).[latex] \displaystyle kg\quad hg\quad dag\quad g\quad d\underbrace{g\quad c}_{1}\underbrace{g\quad m}_{2}g[/latex]
This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: [latex] \displaystyle 1\ dg=1\underbrace{0}_{1}\underbrace{0}_{2}.\ mg[/latex]. The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.[latex] \displaystyle k\underbrace{m\quad h}_{5}\underbrace{m\quad d}_{4}\underbrace{am\quad }_{3}\underbrace{m\quad d}_{2}\underbrace{m\quad c}_{1}m\quad mm[/latex]
Note that instead of moving to the right, you are now moving to the leftso the decimal point must do the same:[latex] \displaystyle 1\ cm=0.\underbrace{0}_{5}\underbrace{0}_{4}\underbrace{0}_{3}\underbrace{0}_{2}\underbrace{1}_{1}\ km[/latex].
Try It
How many milliliters are in 1 liter?Answer: There are 10 milliliters in a centiliter, 10 centiliters in a deciliter, and 10 deciliters in a liter. Multiply: [latex]10\cdot10\cdot10[/latex], to find the number of milliliters in a liter, 1,000.
Example
If you have a prescription for 5,000 mg of medicine, and upon getting it filled, the dosage reads 5g of medicine, did the pharmacist make a mistake?Answer: Convert mg to g.
[latex]5,000\text{ mg}=\text{___ g}[/latex]
[latex] \displaystyle \frac{5,000\text{ mg}}{1}\cdot \frac{1\text{ g}}{1,000\text{ mg}}=\text{ g}[/latex]
[latex] \displaystyle \frac{5,000\cancel{\text{mg}}}{1}\cdot \frac{1\text{ g}}{1,000\ \cancel{\text{mg}}}=\text{ g}[/latex]
[latex] \displaystyle \frac{5,000\cdot 1\text{ g}}{1\cdot 1,000}=\frac{5,000\text{ g}}{1,000}[/latex]
[latex] \displaystyle \frac{5,000\text{ g}}{1,000}=5\text{ g}[/latex]
[latex]5\text{ g}=5,000\text{ mg}[/latex], so the pharmacist did not make a mistake.Licenses & Attributions
CC licensed content, Original
- Question ID 126793, 126794. 126795. Provided by: Lumen Learning License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.