Physics 101 - Conversions And Powers Of Ten Exercise
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2Physics 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
9
giga
G
one billion
1 000 000 000
1 x 10
6
mega
M
one million
1 000 000
1 x 10
3
kilo
k
one thousand
1 000
1 x 10
2
hecto
h
one hundred
100
1 x 10
1
deka
da
ten
10
1 x 10
0
one
1
1 x 10
-1
deci
d
one tenth
0.1
1 x 10
-2
centi
c
one hundredth
0.01
1 x 10
-3
milli
m
one thousandth
0.001
1 x 10
-6
μ
micro
one millionth
0.000 001
1 x 10
-9
nano
n
one billionth
0.000 000 001
1 x 10
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)
10
gram
-1
b. 100 meters = ____________________
________________________
c. 0.000001 liter = __________________
________________________
d. one billion liters = ________________
________________________
e. 10 grams = ______________________
________________________
f. 0.001 meter = ____________________
________________________
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