1. Customary and Metric Units
Lesson 4.3.1

2. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
California Standards:
Algebra and Functions 2.1
Convert one unit of measurement to another (for example, from feet to miles, from centimeters to inches).
Mathematical Reasoning 3.1
Evaluate the reasonableness of the solution in the context of the original situation.
What it means for you:
You’ll see how to convert between different units within the customary or metric systems. For example, feet to inches, or meters to kilometers.
Key words:
conversion
customary system
metric system
unit
conversion table
conversion factor

3. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
This Lesson, you’ll learn how to convert between units in either the customary or the metric system.
So you take a length in inches, say, and convert it to feet.
Or maybe you know a length in centimeters and you need to convert it to kilometers. That kind of thing…

4. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Customary Lengths Are Inches, Feet, Yards, and Miles
The customary system of lengths is the system that uses inches, feet, yards, and miles.
This conversion table shows how many of one unit make up another kind of unit.
Customary lengths
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 1760 yards (yd)
You can use it to convert a measurement in one unit to a measurement in another unit.
The numbers in a conversion table (12, 3, and 1760 in the above table) are sometimes called conversion factors.

5. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Example 1
A vase is 1 yard tall. What is its height in:
(i) feet?
(ii) inches?
Solution
(i) Using the conversion table, you can see that 1 yard is 3 feet.
Customary lengths
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 1760 yards (yd)
(ii) If 1 foot is 12 inches, then 3 feet must be 3 × 12 = 36 inches.
Solution follows…

6. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Notice that when you convert to a smaller unit, the number gets bigger.
This makes sense… the smaller each unit, the more of them you need to cover the same distance.
In fact, if your conversion factor is greater than 1:
● you multiply by it to convert to a smaller unit, since this gives you a bigger number.
● you divide by it to convert to a bigger unit, since this gives you a smaller number.

7. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Example 2
Convert:
(i) 3 miles to yards,
(ii) 7920 yards to miles.
Customary lengths
1 foot (ft) = 12 inches (in.)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 1760 yards (yd)
Solution
There are 1760 yards in a mile, so use 1760 as your conversion factor.
(i) Yards are smaller than miles, so 3 miles = 3 × = 5280 yd.
(ii) Miles are bigger than yards: 7920 yd = 7920 ÷ = 4.5 miles.
Solution follows…

8. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
This diagram summarizes how to convert between customary lengths.
To get from miles to inches, first × by 1760,
× 12
then × by 3,
then × by 12.
÷ 12
× 3
× 1760
÷ 3
To get from inches to miles, first ÷ by 12,
÷ 1760
then ÷ by 3,
then ÷ by 1760.

9. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Guided Practice
Convert:
1. 7 miles to yards yards to miles
3. 72 inches to feet feet to yards
5. 5 feet to inches 6. 9 yards to inches
7. 1 mile to feet 8. 8 yards to inches
7 × 1760 = 12,320 yd
8800 ÷ 1760 = 5 mi
72 ÷ 12 = 6 ft
12 ÷ 3 = 4 yd
5 × 12 = 60 in.
9 × 3 = 27 ft
27 × 12 = 324 in.
1 × 1760 = 1760 yd
1760 × 3 = 5280 ft
8 × 3 = 24 ft
24 × 12 = 288 in.
Solution follows…

10. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Guided Practice
Convert:
9. 2 miles to inches ,000 inches to miles 1 3
2 × 1760 = 3520 yd
3520 × 3 = 10,560 ft
10,560 × 12 = 126,720 in.
100,000 ÷ 12 = 8333
÷ 3 = 2777
÷ 1760 = mi 1 3 7 9
11. If Letitia cycles 3 miles, how many feet has she gone? 7 9
3 × 1760 = 5280 yd
5280 × 3 = 15,840 ft
12. Mount Whitney is 14,494 feet tall. How many miles is this? 1 3
14,494 ÷ 3 = yd
÷ 1760 = mi 1 3
Solution follows…

11. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
The Metric System Is Based on the Meter
The metric system of lengths is based on the meter.
All metric units for length contain the word “meter” — millimeter, centimeter, decimeter…
Here’s a conversion table.
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
These are all bigger than meters.
These are all smaller than meters.
Notice that some of the conversion factors are less than one.

12. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Example 3
Convert 120 meters to millimeters.
Solution
You’re converting from a big unit (meters) to a smaller one (millimeters), so the number needs to be bigger.
The conversion factor is (1 mm = m).
This is less than 1, so to make a bigger number, you need to divide by the conversion factor.
120 m = 120 ÷ = 120 × 1000 = 120,000 mm
Solution follows…

13. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Example 4
A pencil is 10 cm long. How long is the pencil in kilometers?
Solution
First, convert 10 cm to meters by multiplying by 0.01.
This gives a smaller number: 10 centimeters = 10 × 0.01 = 0.1 m
Next, convert 0.1 m to kilometers by dividing by 1000.
This also gives a smaller number: 0.1 m = 0.1 ÷ 1000 = km
Solution follows…

14. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
This diagram summarizes how to convert between metric lengths.
Multiply by 10 to convert one step smaller.
× 10
Multiply by 100 to convert two steps smaller, etc…
× 10
÷ 10
× 10
÷ 10
Divide by 10 to convert one step bigger.
÷ 10
÷ 10
÷ 10
Divide by 100 to convert two steps bigger, etc…
÷ 10
× 10
× 10
× 10

15. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Guided Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
Convert:
13. 7 km to m m to km
mm to cm cm to mm
m to km ,000 m to km
7 × 1000 = 7000 m
8700 ÷ 1000 = 8.7 km
85 ÷ 10 = 8.5 cm
120 × 10 = 1200 mm
180 ÷ 1000 = 0.18 km
15,000 ÷ 1000 = 15 km
Solution follows…

16. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Guided Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
Convert:
km to m mm to cm
0.1 × 1000 = 100 m
160 ÷ 10 = 16 cm
21. A snail moves 3 m. How many cm is this?
3 × 100 = 300 cm
Solution follows…

17. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Independent Practice
There are 12 inches in 1 foot, meaning the conversion factor is 12.
1. Would you divide by 12 or multiply by 12 when converting from feet to inches?
Multiply
2. Would you divide by 12 or multiply by 12 when converting from inches to feet?
Divide
Solution follows…

18. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
3. How would you convert from yards to miles?
Divide by 1760
In Exercises 4–9, find the missing values in the conversions.
4. 36 in. = ? yd in. = ? yd ft = ? yd
yd = ? ft ft = ? yd mi = ? ft 1 4 9
300 33
1320
Solution follows…

19. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
10. TJ’s guitar is 3.5 ft long. What is the length of the guitar in inches?
42 in.
11. Would you divide by 100 or multiply by 100 when converting from meters to centimeters?
Multiply by 100
Solution follows…

20. Divide by 100,000 (but multiply by 0.00001)
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
12. There are 1000 millimeters in a meter, and 100 meters in a hectometer. What is the conversion factor when converting millimeters to hectometers?
100,000 (or )
13. Would you multiply or divide by this conversion factor when converting millimeters to hectometers?
Divide by 100,000 (but multiply by )
Solution follows…

21. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
Find the missing value in Exercises 14–19.
m = ? cm km = ? m
mm = ? cm cm = ? m
18. 4 dam = ? dm dm = ? mm
3000
2000 25
0.005
400 37
Solution follows…

22. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
20. An Olympic swimming pool has a length of 50 meters. What is this distance in kilometers?
0.05 km
The length of the wingspan of an airplane is 40 m.
21. Find the wingspan of this airplane in centimeters.
4000 cm
22. Find the wingspan of this airplane in kilometers.
0.04 km
Solution follows…

23. Ying’s (the actual number is 126,720)
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
A compact disc has a diameter of 120 millimeters.
23. What is the diameter of a compact disc in centimeters?
12 cm
24. What is the diameter of a compact disc in decimeters?
1.2 dm
25. Ying and Carol jog exactly 2 miles together every Saturday. They both guess how many inches their jog is. Ying guessed 100,000 in. and Carol guessed 10,000 in. Whose guess is closer to the actual amount?
Ying’s (the actual number is 126,720)
Solution follows…

24. 1,000,000,000 (1 billion) micrometers
Lesson
4.3.1
Customary and Metric Units
Independent Practice
Metric lengths
1 dekameter (dam) = 10 meters
1 hectometer (hm) = 100 meters
1 kilometer (km) = 1000 meters
1 decimeter (dm) = 0.1 meters
1 centimeter (cm) = 0.01 meters
1 millimeter (mm) = meters
Micrometers are metric units that can be used to measure very small objects. In fact, 1 millimeter is equal to 1000 micrometers.
26. How many micrometers are in 0.25 millimeters?
250 micrometers
27. How many micrometers are in 1 kilometer?
1,000,000,000 (1 billion) micrometers
Solution follows…

25. Customary and Metric Units
Lesson
4.3.1
Customary and Metric Units
Round Up
So to convert something from one unit to another, you need to make the number either bigger (if you’re converting to a smaller unit) or smaller (if you’re converting to a bigger unit).
Conversion factors are useful, but you have to use them sensibly.
There’s more on conversions next Lesson.