Quantities and Units Used in the International System (SI) (aka the metric system)
NOTE: There are additional quantities used in science but these are the quantities we will be
using in this course.
Quantity
Unit and Symbol
mass
gram (g), kilogram (kg), centigram (cg), milligram (mg)
length
meter (m), kilometer (km), centimeter (cm), millimeter (mm)
volume
liter (L), milliliter (mL)
cubic centimeter (cm3), cubic decimeter (dm3)
energy
joule (J), kilojoule (kJ)
time
second (s)
temperature
Celsius (oC), Kelvin (K)
density
for solids and liquids: g/mL, g/cm3
for gases: g/L, g/dm3
specific heat
J
(g)(oC)
pressure
millimeters of mercury (mmHg); atmosphere (atm); Pascal (Pa);
The SI system uses prefixes in front of the base unit:
milli- means
1
1 000
of the base unit; ex.: 1 000 mm = 1 m
centi- means
1
100
of the base unit; ex.: 100 cg = 1 g
kilo- means 1000 x the base unit; ex.: 1 kJ = 1 000 J
or 1 mm = 0.001 m
or 1 cg = 0.01 g
or
1 J = 0.001 kJ
Left to right, from largest unit to smallest unit:
kilo- (1000 base units)
hecta- (100 base units)
deka- (10 base units)
base unit (1 base units)
deci- (1/10 of a base unit)
centi- (1/100 of a base unit)
milli- (1/1000 of a base unit)
The prefixes remain the same regardless of which base unit you use.
1 000 mm = 1 m
1 000 mL = 1 L
1 000 mg = 1 g
Note that there is no “comma” after the number “1” in the number one thousand. In the rest of
the world, the “comma” is used to represent a decimal point. Therefore, numbers are simply
written in groups of three with no commas and only one decimal point: 54 775 890.115 07
Writing numbers this way makes it easier to read the number.
The prefixes we will use most frequently are: kilo- , centi- , deci- , and milli- .
Relationships between these prefixes are:
10 milli - = 1 centi -
10 mm = 1 cm
1 000 mill- = 1 base unit
1 000 mm = 1 m
100 centi- = 1 base unit
100 cm = 1 m
10 centi- =
10 dm
=
1 deci-
10 cm = 1 dm
1 base unit
10 dm = 1 m
1000 base unit = 1 kilo-
1 000 m = 1 km
To convert from one unit to another, we use conversion factors. To make conversion factors,
first write the equality between the unit you have and the unit you want.
Example #1: to convert 45 mm to cm, the equality between mm and cm is:
10 mm = 1 cm
Now write two conversion factors using the equality:
_1 cm__
10 mm
10 mm
1 cm
and
Write the value you have and select the one conversion factor that will allow you to cancel the
unit you have. Remember, you can only cancel units between a numerator and a denominator
within a fraction or across a multiplication sign. Cancel the matching units.
45 mm x __1 cm__
10 mm
=
4.5 cm
Example #2: convert 45 kg to mg
We’ll use two equalities: 1 000 mg = 1 g
45 kg x _1 000 g__ x
1 kg
and
1 000 mg_
1 g
1 000 g = 1 kg
= 4 500 000 mg or 4.5 x 106 mg
Convert each of the following units to the requested unit. Show all work.
1. 25 g to kg
2. 36 kg to g
3. 5 kg to cg
4.
625 cg to kg
5.
533 cg to mg
6.
287 mg to cg
7.
946 mg to g
8.
154 g to mg
9.
269 mm to km
10. 15 km to mm
11. 0.5 kL to L
12. 14 mL to L
13.
1 457 mm to km
14. 2.53 cm to m