Some of the content of this guide was modeled after a guide originally created by Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY NC SA 4.0 International License.
Metric and the International System of Units (Système International or SI) are measurement systems consisting of base units and prefixes. The base units are defined for measurable properties and the prefixes describe varied sizes of units within each base unit.
Because of the similarities, the two systems are often used together and regarded as being the same system. However, there are some subtle differences. The definitions of SI base units are based on unchanging fundamental properties of nature while metric base units are less stringently defined. The metric system also includes derived units where SI does not.
| Fun Fact |
|---|
|
The metric system was first adopted in France in 1795. SI was derived from the metric system in 1960 to express properties more complicated than length, weight, and volume. |
Quirks of SI
Kilogram is the only base unit that has a prefix.
There are no base units for area or volume. Area and volume are calculated units determined by the dimensions of a space or object.
SI and metric base units are often used together and there is some overlap in the two systems.
|
Physical Property |
Unit |
Symbol |
|
Amount of a substance |
mole |
mol |
|
Electric current |
ampere |
amp |
|
Length |
meter |
m |
|
Luminous intensity |
candela |
cd |
|
Mass |
kilogram |
kg |
|
Temperature |
kelvin |
K |
|
Time |
second |
s |
|
Physical Property |
Unit |
Symbol |
|
Length |
metre |
m |
|
Area |
square metre |
m2 |
|
Volume |
cubic metre |
m3 |
|
Weight |
gram |
g |
|
Capacity |
litre |
L |
|
Temperature |
degree Celsius |
℃ |
Prefixes are useful when talking about very large and very small numbers. It would be difficult to measure the distance from Vancouver, Canada to Paris, France using centimetres. Kilometres are more useful in that case. But kilometers or metres would be a poor choice for measuring the dimensions of a book.
|
Name |
Symbol |
Base 10 multiplier |
Decimal |
|
|
peta |
P |
1015 |
1000000000000000 |
⬆ bigger —
smaller ⬇
|
|
tera |
T |
1012 |
1000000000000 |
|
|
giga |
G |
109 |
1000000000 |
|
|
mega |
M |
106 |
1000000 |
|
|
kilo |
k |
103 |
1000 |
|
|
hecto |
h |
102 |
100 |
|
|
deca |
da |
101 |
10 |
|
|
— |
— |
100 |
1 |
|
|
deci |
d |
10−1 |
0.1 |
|
|
centi |
c |
10−2 |
0.01 |
|
|
milli |
m |
10−3 |
0.001 |
|
|
micro |
μ |
10−6 |
0.000001 |
|
|
nano |
n |
10−9 |
0.000000001 |
|
|
pico |
p |
10−12 |
0.000000000001 |
|
|
femto |
f |
10−15 |
0.000000000000001 |
Caution! A conversion diagram works well for the prefixes shown in the image above because the base 10 multipliers are consecutive (10-3, 10-2, 10-1, 100 (base unit), 101, 102, 103). When micro (10-6) and mega (106) are added it looks like the decimal should move for spaces, but it actually needs to move six spaces. See the Decimal Conversion section below for a broader application of the principles behind the Conversion Diagram method.
Example I
Convert 12.52 L to mL
To go from L to mL, you have to move three times to the left. Therefore, move the decimal three times to the right.
Method 1
Moving the decimal three places to the right gives:
Method 2
Since you moved three spaces to the left to get to ml on the diagram divide the value by ten to the power of minus three (10-3).
Have questions about how the ten to the power of three became positive? Check out this guide for more details.
This method of unit conversion involves moving the decimal point of a measurement, much like using a conversion diagram. Both methods work because the prefixes are related to each other by factors of ten. The decimal conversion method outlined here addresses the limitation of conversion diagrams noted in the Caution! in the section above.
There are two pieces of knowledge required to understand decimal conversion. You will need to know the base 10 multipliers for the prefixes. You will also need to know how to divide exponents.
|
Step |
Action |
Example |
|
1 |
Determine the direction that the decimal needs to move. The relative unit size determines the direction.
Is the desired unit smaller or larger than the starting unit?
|
Convert 0.274 hectometres (hm) to centimetres (cm).
starting prefix: hecto = 102 (larger) desired prefix: centi = 10-2 (smaller)
The desired unit size is smaller so the decimal must move to the right. |
|
2 |
Determine the number of places the decimal must move. The base 10 multipliers determine the decimal places.
Divide the base 10 multiplier of the larger unit by the multiplier of the smaller unit. The resulting exponent is the number of places the decimal must move.
|
hecto = 102 (larger) centi = 10-2 (smaller)
The decimal must move 4 places. |
|
3 |
Move the decimal and add zeros as needed. |
0.274 hm = 2740 cm
|
|
4 |
Check: When the unit gets smaller, the value gets larger. When the unit gets larger, the value gets smaller. |
The example went from a larger unit (hm) to a smaller one (cm), so the value for the desired unit should be larger.
And it is! 2740 > 0.274
|
Area (m2) and Volume (m3)
The process to convert the squared or cubic units of area and volume has an additional part to step 2 shown above. Because these units have more than one length parameter (e.g. squared has two lengths), we must account for that in unit conversions.
Example: Convert 1000000 cm3 to m3.
We can think of this in terms of the three length parameters that make up a cubit centimetre (cm3).
100 cm x 100 cm x 100 cm = 1000000 cm3
If we convert each centimetre length to metres, then multiply, we get cubic meters (m3).
100 cm = 1 m
1 m x 1 m x 1 m = 1 m3
So, 1000000 cm3 = 1 m3. To do this more simply, multiply the value obtained in step 2 above by either 3 (for squared units) or 3 (for cubic units). For the example, metres are larger than centimetres so the decimal must move to the left.
With simple units, we would move the decimal 2 places, but these are cubic units so we need to multiply by 3 to determine the number of places to move the decimal. 2 x 3 = 6, so the decimal must move 6 places.
So, 1000000 cm3 = 1 m3
Example: Convert 2.382 m3 to cm3.
Centimetres are smaller than metres so the decimal must move to the right.
These are cubic units, so we need to multiply by 3 to determine the number of places to move the decimal. The decimal must move 6 places.
2.382 m3 = 2382000 cm3
To maintain the four significant digits, the answer can be written as 2.382 x 106 cm3.
Quick and Sneaky Tip
When converting from any prefixed unit to the base unit, you can simply replace the prefix with its base 10 multiplier and simplify as needed.
Example: Convert 4987 cm to m.
The base 10 multiplier for centi is 10-2 so 4987 cm = 4987 x 10-2 m
| Units of length in the metric system | Units of weight in the metric system | Units of volume in the metric system |
|
1,000 millimeters (mm) = 1 meter 100 centimeters (cm) = 1 meter 10 decimeters (dm) = 1 meter 1 dekameter (dam) = 10 meters 1 hectometer (hm) = 100 meters 1 kilometer (km) = 1000 meters |
1 gram = 1,000 milligrams (mg) 1 gram = 100 centigrams (cg) 1 kilogram (kg) = 1,000 grams 1 metric ton (t) = 1,000 kilograms |
1 cc = 1 cm3 1 milliliter (mL) = 1 cm3 1 liter (L) = 1,000 millimeters (mL) 1 hectoliter (hL) = 100 liters (L) 1 kiloliter (kL) = 1,000 liters (L) |
Example 1
Convert 42.50 m to km
Step 1 : Write the conversion factor from the table above.
1 kilometer (km) = 1000 meters (m)
Step 2 : Write the conversion factor as a ratio.
Since we are converting meters to kilometers, write the km on the top and m on the bottom, as shown below:
Step 3: Multiply 42.50m by the above ratio.
Then the answer becomes 0.04250 km with four significant digits.
** Notice how the "m" on the top and the "m" at the bottom cancel out to give "km" as the final unit, as seen below:
A unit conversion calculator can be used to verify your answers.
Want to check your understanding? Try our online Quiz!
