Measurement: Converting Distances

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1 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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2 -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 = x ft.

12 in. = 1 ft

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3 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. = x ft.

1 yd. = 3 ft.

Let’s cross multiply.

7 x 3 = 21 1 x x = 1 x

21 = 1x

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4 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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5 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 2. 500 dekameters = x decimeters

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6 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 Abbreviation English Abbreviation

Kilometer km Miles mi

Hectometer hm Yards yd

Dekameter dam Feet ft

Meter m Inches in

Decimeter dm

Centimeter cm

Millimeter mm

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7 Directions: Convert each value using the English System to find the value of x.

1. 44 mi. = x ft. 2. 240 in. = x ft. 3. 10 yd. = x in.

x = x = 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 11. 27,019 cm = f dam 12. 217 km = f m f = f = f =

13. 8,000 mm = f km 14. 30,500 hm = f dm 15. 6 m = f dm f = f = f =

16. 27 mm = f cm 17. 2000 dm = f dam 18. 95 m = f hm

f = f = f =

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8 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

Measurement: Converting Distances

1

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

2

-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 = x ft.

12 in. = 1 ft

3

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. = x ft.

1 yd. = 3 ft.

Let’s cross multiply.

7 x 3 = 21 1 x x = 1 x

21 = 1x

4

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

5

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 2. 500 dekameters = x decimeters

7 yards = _ feet (once again lets use x to represent __)

x = x = x =

x = x = x =

x = x = x =

10. 10 hm = f mm 11. 27,019 cm = f dam 12. 217 km = f m f = f = f =

13. 8,000 mm = f km 14. 30,500 hm = f dm 15. 6 m = f dm f = f = f =

f = f = f =