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Measurement: Converting Distances
Measuring Distances
Measuring distances is done by measuring length. You may use a different system to
measure length differently than other places in the world. This is because there is more
than one system you can use.
The United States uses something called the English system. Other countries use
something called the Metric system instead. The U.S. uses the Metric system
sometimes. Yet in the U.S., English is the system that is used most often.
Runners and cyclists travel yards, miles, or meters. These are all distances. Yards and
miles are English system measurements. A meter is the standard unit (for length) of the
Metric system.
Each system is unique. The reason the United States has not converted over to the
Metric system is simple. So many people know the English system and it is still taught in
schools. Scientists hope one day there will be one universal system that is used across
the world.
The English System
You should already recognize units in the English system. If you have ever measured
anything with a ruler or traveled in a car then you have used the English system.
The English system measures length by inches, feet, yards, and miles.
-Inches 1 foot = 12 inches
1 yard = 36 inches
1 mile = 63,360 inches
-Foot-
12 inches = 1 foot
1 yard = 3 feet
1 mile = 5,280 feet
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-Yard-
36 inches = 1 yard
3 feet = 1 yard
1 mile = 1,760 yards
-Mile-
63,360 inches = 1 mile
5,280 feet = 1 mile
1,760 yards = 1 mile
Converting using the English system
It is easy to convert between inches, miles, feet, and yards if you know basic math
skills. It is important to know how the values compare so you can convert one distance
value to another.
For example:
48 inches equals ______ feet.
We know that 12 inches = 1 foot. We must make the value of “______ “ a letter until we
know what that letter stands for.
In this problem we will call “______” x.
48 in.
=
x feet
To get the value of x we divide each side by the values we know.
48 in =
12 in. =
2
x ft.
1 ft
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Then we cross multiply.
48 x 1 = 48
12 x x = 12x
12x = 48
We need to isolate x to one side so we divide both sides by the number in front of x.
12x = 48
12
12
x=4
Our answer is = 48 in. is equal to 4 ft.
This method works when converting smaller distances into larger distances:
Note: You would use this when converting inches to feet, inches to yards, inches to
miles, feet to yards, feet to miles, and yards to miles.
If you want to convert a larger distance into a smaller distance this is what you need to
do.
7 yards = _____ feet (once again lets use x to represent ______)
We know that 1 yard = 3 feet.
7 yd. =
1 yd. =
x ft.
3 ft.
Let’s cross multiply.
7 x 3 = 21
1xx=1x
21 = 1x
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21 = x
The answer is 7 yards = 21 feet.
Try these English system conversions on your own to see if you get the right answers,
1. 3 miles = x feet 2. 11 yards = x inches
3. 316,800 inches = x miles
You can check your answers at the end of this lesson.
The Metric System
The Metric system is usually viewed as easier than the English system. In countries like
Canada, the Metric system is the standard system of measurement. Cars do not travel
by miles. Instead, they travel by kilometers.
The standard measurement is a meter. To determine what is being measured the suffix
is placed in front of the word meter.
Here is a box listing Metric values that are the most commonly used.
Metric Value
Numerical Value
Kilo–meter (kilometer)
1000
Hecto-meter (hectometer)
100
Deka-meter (decameter)
10
Meter
1
Deci-meter (decimeter)
0.1
Centi-meter (centimeter)
0.01
Milli-meter (millimeter)
0.001
The way to convert values is easier using the Metric system.
3000 Kilometers = x meters
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To figure this out we move a decimal place to the right if we are going from the top of
the Metric scale to the bottom (i.e. kilometers to a lesser value such as meters or
centimeters).
Since meters are three levels below kilometers in our chart, we move the decimal point
over 3 spaces to the right.
One space to the right is 30,000.
Two places to the right is 300,000.
Three spaces to the right is 3,000,000.
3,000.kilometers is equal to 3,000,000 meters.
The Metric system seems simple, but what if you want to convert a lesser distance into
a larger distance?
2 centimeters = x hectometers
To figure this out we move a decimal place to the left if we are going from the bottom of
the Metric scale to the top (i.e. centimeters to a larger value such as dekameters or
kilometers).
Since hectometers are four levels above centimeters in our chart, we move the decimal
point over 4 spaces to the left.
One space to the left is 0.2
Two places to the left is 0.02
Three spaces to the left is 0.002
Four spaces to the left is 0.0002
2 centimeters is equal to 0.0002 hectometers.
Try doing the following problems on your own and see if you can get the right answers.
1. 1000 millimeters = x kilometers
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2. 500 dekameters = x decimeters
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Answers to sample problems
The answers to our first set of sample problems (the English system) are:
1. 15,840 ft.
2. 396 in.
3. 5 miles
How did you do?
Here are the answers for the second set of sample problems (the Metric system):
1. 0.001 km
2. 50,000 dm
Abbreviations
Both the Metric and English systems use abbreviations to make labeling units easier.
Here is a chart showing the basic abbreviations for both Metric and English system
values.
Metric
Kilometer
Hectometer
Dekameter
Meter
Decimeter
Centimeter
Millimeter
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Abbreviation
km
hm
dam
m
dm
cm
mm
English
Miles
Yards
Feet
Inches
Abbreviation
mi
yd
ft
in
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Measurement: Converting Distances Worksheet
Directions: Convert each value using the English System to find the value of x.
1. 44 mi. = x ft.
x = ____________
2. 240 in. = x ft.
x = ____________
3. 10 yd. = x in.
x = ____________
4. 88,000 yd. = x mi.
5. 5 mi. = x in.
6. 972 in. = x yd.
x = ____________
x = ____________
x = ____________
7. 760,320 in. = x mi.
8. 70 ft.. = x in.
9. 300 in. = x ft.
x = ____________
x = ____________
x = ____________
Directions: Convert each value using the Metric System to find the value of f.
10. 10 hm = f mm
f = ____________
13. 8,000 mm = f km
f = ____________
16. 27 mm = f cm
f = ____________
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11. 27,019 cm = f dam
f = ____________
14. 30,500 hm = f dm
f = ____________
17. 2000 dm = f dam
f = ____________
12. 217 km = f m
f = ____________
15. 6 m = f dm
f = ____________
18. 95 m = f hm
f = ____________
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Answer Key
1. 232,320 ft.
2. 20 ft.
3. 360 in.
4. 50 mi.
5. 316,800 in.
6. 27 yd.
7. 12 mi.
8. 840 in.
9. 25 ft.
10. 1,000,000 mm
11. 27.019 dam
12. 217,000 m
13. 0.008 km
14. 30,500,000 dm
15. 60 dm
16. 2.7 cm
17. 20 dam
18. 0.95 hm
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