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Converting Units
Sometimes it is useful for measurements to be expressed in different units as were originally used. Instead of
taking the measurement over again in the desired unit, it is often easier to convert the unit using conversion
factors. In this worksheet you will practice constructing conversion factors and using them in unit
conversion problems.
CONVERSION FACTORS
Conversion factors are ratios of two equivalent (they are equal to each other) measurements. The numbers of
each measurement may not be the same, but both measurements (each with both its number and unit) are the
same. For example, 100 centimeters (cm) is equal in length to 1 meter (m). Because these measurements are
equal to each other, a conversion factor can be constructed from them. Units are displayed using their
abbreviations. Below are the two possibilities for the ratio between 100 cm and 1 m:
100 cm
1m
1m
100 cm
Conversion factors can be unusual too. For example, 1 football field (fbf) is 100 yards (yd) long. This can
also be stated as “1 football field is equal to 100 yards” or “1 football field is equivalent to 100 yards”. The
conversion factors between these two measurements would then be:
1 fbf
100 yd
100 yd
1 fbf
Complete the following questions to create conversion factors:
1. 10 millimeters (mm) is equivalent to 1 centimeter (cm). Write the two conversion factors that can be
constructed from these measurements in the space below.
2. 1 kilogram (kg) has a mass equal to 1000 grams (g). Write the two conversion factors that can be
constructed from these measurements in the space below.
3. Complete the blanks in the statement below, and then write the two conversion factors that can be
constructed from the measurements.
_______________ second (s) is equivalent to _______________ minutes (min)
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4. Complete the blanks in the statement below, and then write the two conversion factors that can be
constructed from the measurements.
_______________ minutes (min) is equivalent to _______________ hour (hr)
If a chart of SI Prefixes happens to be handy (such as the chart on textbook page 26) it is easy to construct
conversion factors between measurements with these prefixes. What if, for example, a conversion factor
between millimeters (mm) and centimeters (cm) was desired? First the number associated with each prefix
should be determined. For millimeters, the prefix is milli- while for centimeters the prefix is centi-. The
number for each prefix is determined below (Note: The number for a unit without a prefix, such as just
meter, is 1):
Prefix
millicenti-
Number
0.001
0.01
To construct the conversion factor between millimeters and centimeters we pair up the smaller number with
the greater unit and the greater number with the smaller unit. What does this mean exactly? Well, it is easy
to see that the smaller number from above is 0.001 and that 0.01 is larger. Likewise, the larger unit is the
one with the larger number (in the chart). So this means that centimeters is larger than millimeters. Now to
create the conversion factor you must pair the smaller number with the larger unit and the larger number
with the smaller unit. See the example of one of the conversion factors below:
Smaller
number
Larger
number
centimeter s
0.01 millimeter s
0.001
Larger
unit
Smaller
unit
The two conversion factor between centimeters and millimeters would then be as follows:
0.01 mm
0.001 cm
0.001 cm
0.01 mm
Determine the requested conversion factors below. First determine the prefixes and number associated with
them. Then determine the conversion factors. Use Figure 15 on textbook page 17.
5. Conversion factors between kilograms and milligrams.
Larger prefix: ______________ Larger number: ______________
Smaller prefix: ______________ Smaller number: ______________
Conversion Factors:
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Name ____________________ Student Number ______ Date _____________
6. Conversion factors between millimeters and kilometers.
Larger prefix: ______________ Larger number: ______________
Smaller prefix: ______________ Smaller number: ______________
Conversion Factors:
7. Conversion factors between nanoseconds and milliseconds.
Larger prefix: ______________ Larger number: ______________
Smaller prefix: ______________ Smaller number: ______________
Conversion Factors:
8. Conversion factors between grams and micrograms.
Larger prefix: ______________ Larger number: ______________
Smaller prefix: ______________ Smaller number: ______________
Conversion Factors:
SIMPLE CONVERSION PROBLEMS
It is a good science skill to be able to construct conversion factors. But why? To successfully complete unit
conversion problems of course! Conversion factors convert one unit into another. It is important to
understand that the factor does not change the measurement but only its number and its unit. Follow the
steps below to complete conversion problems. An example is given on the next page.
Conversion Problem Steps
STEP 1 – Set up both unit conversion factors between the units you are converting between. Chose the factor containing the
unit you are converting from on the bottom. Circle it.
STEP 2 - Put the starting measurement (the measurement you are converting from) over 1.
STEP 3 – Multiply the starting measurement (from step 2) by the chosen conversion factor (from step 1). Cancel everything
that appears both on the top and bottom in the equation (both numbers and units).
STEP 4 - Calculate the problem, including the units!
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Simple Conversion Problem Example
Problem: Convert 45 centimeters to millimeters
STEP 1 – Set up both unit conversion factors between the units you are converting between. Chose
the factor containing the unit you are converting from on the bottom. Circle it.
0.001 cm
0.01 mm
0.01 mm
0.001 cm
STEP 2 - Put the starting measurement (the value you are converting from) in the problem over 1.
45 cm
1
STEP 3 – Multiply the starting measurement by the chosen conversion factor. Cancel everything that
appears both on the top and bottom in the equation (both numbers and units).
45 cm 0.01 mm
×
=
1
0.001 cm
STEP 4 - Calculate the problem, including the units!
45 cm 0.01 mm 45(0.01) mm 450 mm
×
=
=
= 450 mm
1
0.001 cm
0.001
1
Using the four steps above, complete the following conversion factors. Pay special attention to step one and
write down both conversion factors before completing the problem.
9. Convert 4 meters to centimeters.
10. Convert 453 grams to kilograms.
11. Convert 150 seconds to minutes.
12. Convert 2 meters and 33 centimeters to centimeters.