Physics 101 – Conversions and Powers of Ten Exercise
The purpose of this exercise is to become familiar with how to convert between units and power of ten
notations.
Conversions
Scientists use the International System of Measurement (S.I. units) when making measurements. This
is a modern adaptation of the metric system (using meters, kilograms, and liters), and it is used by
nearly all of the people in the world. Because S.I. units are based on multiples of 10, it is very straight
forward to convert between the SI units and prefixes. In this activity, you will practice changing units
to larger or smaller prefixes and powers.
The basic S.I. units for length, volume, and mass are meter (m), liter (L), and gram (g). These units
often have prefixes added to them to form units that are larger or smaller. Some of the prefixes are
listed in the table below:
Prefix
Symbol
Value
Numeric Value
Power of Ten Notation
giga
G
one billion
1 000 000 000
1 x 10
mega
kilo
M
k
one million
one thousand
1 000 000
1 000
1 x 10
3
1 x 10
hecto
h
one hundred
100
1 x 10
2
deka
da
ten
10
1 x 10
1
one
1
1 x 10
0
9
6
deci
d
one tenth
0.1
1 x 10
-1
centi
c
one hundredth
0.01
1 x 10
-2
milli
m
one thousandth
0.001
1 x 10
-3
micro
nano
μ
n
one millionth
one billionth
0.000 001
0.000 000 001
1 x 10
-9
1 x 10
-6
Note:
 There is no prefix that means one. For example, a liter is simply L.
 Capital letters make a difference. Make sure that you use the proper case.
 The letter m is used often. Lower case m means meter or the prefix milli- (so that a millimeter
is mm). The prefix micro- uses the Greek letter µ.
 Prefixes do not exist for every value. For example, there is no prefix that means 10,000 or
100,000.
1. Convert to the prefix with units that goes with the value of 1, the abbreviation of the new unit, and
the power of ten notation with the base unit that is the equivalent to each value below. The first one
has been done for you:
a. 0.1 gram =
1 decigram (dg)
b. 100 meters = ____________________
c. 0.000001 liter = __________________
d. one billion liters = ________________
e. 10 grams = ______________________
f. 0.001 meter = ____________________
10-1 gram
________________________
________________________
________________________
________________________
________________________
To convert S.I. prefixes, you can use multiplication and division, for example:
1 kg = 1000 g, so 2 kg = 2 x 1000 g = 2000 g
1 m = 1/1000 km or 0.001 km, so 2 m = 2 x (1/1000 km) or 2 x 0.001 km = 0.002 km
Using the method above complete the following:
1 microgram (μg) = ______________________ g
20 kilometers (km) = _____________________m
5 centimeters (cm) = _____________________ mm
2. Another way to convert S.I. prefixes and powers is to move the decimal point a particular number
of places. This is easiest done by writing out the units from largest to smallest. This is done below
for you using the mass unit gram (g), with spaces left for values that have no prefix.
Gg
Mg
kg
hg
dag
g
dg
cg
mg
μg
ng
When you convert, look at the direction and number of spaces moved on the grid above. This will
tell you the direction and number of spaces that the decimal point should move. For example, to
convert from Megagrams (Mg) to decigrams (d)g the decimal would move to the right seven
spaces. This procedure will work for any S.I. prefix, not only for grams.
Convert the S.I. prefixes below. The first one has been done for you:
a). 0.00028 mg =
0.28 __________µg
b) 226 cg = ___________________ g
c) 9.4 kg = ___________________ dag
d) 5400 mL = _________________ L
e). 2.73 hL = __________________ dL
f). 436 mm = __________________ m
g) 32.8 Mm = _________________ cm
3. The area of a rectangle is calculated by multiplying the length of one side by that of the other. In
other words, length x width or vice versa. By knowing the area of a table in meters, convert to the
other two units given below:
A = _____100_____________ m2
A = __________________ cm2
A = __________________ in2 (1 in = 2.54 cm)
Physics 101 - Conversions and Powers of Ten Exercise
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