1. Converting Between Unit Systems
Lesson 4.3.3

2. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
California Standard:
Algebra and Functions 2.1
Convert one unit of measurement to another (for example, from feet to miles, from centimeters to inches).
What it means for you:
You’ll convert between the customary and metric unit systems.
Key words:
customary system
metric system
conversion

3. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
So far, you’ve converted metric units to other metric units, and customary units to other customary units.
This Lesson, you’ll use conversion tables for converting between the two unit systems.
You’ll see that all the techniques from the previous Lessons work in exactly the same way in this Lesson too.

4. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Use the Conversion Tables to Help You
The tables below show conversion factors you can use to convert between customary and metric units.
Customary to Metric
Metric to Customary
1 inch (in.) = 2.54 cm
1 cm = 0.39 inches (in.)
1 foot (ft) = cm
1 cm = feet (ft)
1 yard (yd) = 0.91 m
1 m = 1.09 yards (yd)
1 mile (mi) = 1.61 km
1 km = 0.62 miles (mi)

5. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Customary to Metric
1 inch (in.) = 2.54 cm
1 foot (ft) = cm
1 yard (yd) = 0.91 m
1 mile (mi) = 1.61 km
You can convert feet to centimeters by multiplying by (to give you a bigger number, since feet are bigger than centimeters).
But you can also convert feet to centimeters by dividing by (which also gives you a bigger number, since is less than 1).
Metric to Customary
1 cm = 0.39 inches (in.)
1 cm = feet (ft)
1 m = 1.09 yards (yd)
1 km = 0.62 miles (mi)
So you only really need one of the conversion tables. If you know the conversion factors in one table, you can use them to convert from metric to customary or from customary to metric.

6. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 1
Convert 10 km to miles.
Solution
There are two ways you could use the tables to get your answer.
(i) Multiply by 0.62 (to get a smaller number, since miles are a bigger unit than kilometers).
So 10 km = 10 × 0.62 miles = 6.2 miles
(ii) Divide by 1.61.
So 10 km = 10 ÷ 1.61 miles = 6.21 miles (to 2 decimal places)
Solution follows…

7. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 2
Convert 1 mile to meters.
Solution
Customary to Metric
1 inch (in.) = 2.54 cm
1 foot (ft) = cm
1 yard (yd) = 0.91 m
1 mile (mi) = 1.61 km
From the table, you can see that 1 mile is 1.61 km.
And you’ve already seen that to convert kilometers to meters you multiply by 1000.
So 1 mile = 1.61 × 1000 meters = 1610 meters.
Solution follows…

8. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
× 10
× 2.54 or ÷ 0.39
÷ 10
÷ 2.54 or × 0.39
× 12
This diagram might be helpful for some conversion questions.
÷ 12
÷ 3
÷ 1.09 or × 0.91
× 3
÷ 1000
÷ 1.61 or × 0.62
× 1.09 or ÷ 0.91
× 1000
× 1.61 or ÷ 0.62

9. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Most of the conversion factors for converting between metric and customary systems are only approximations.
Most of them are only given to two decimal places.
This means your answer won’t always be exact.
You can sometimes get slightly different answers if you do the question in different ways.

10. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 3
Convert 1 yard into meters by:
(i) converting yards to inches, inches to centimeters, and then centimeters to meters,
(ii) using the conversion factor 0.91,
(iii) using the conversion factor 1.09.
Comment on your answers.
Solution
(i) Do the conversion in three stages:
1) yards to inches: 1 yard = 36 inches
2) inches to cm: 36 inches = 36 × 2.54 cm = cm
3) cm to meters: cm = ÷ 100 m = m
Solution continues…
Solution follows…

11. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 3
Convert 1 yard into meters by:
(i) converting yards to inches, inches to centimeters, and then centimeters to meters,
(ii) using the conversion factor 0.91,
(iii) using the conversion factor 1.09.
Comment on your answers.
Solution (continued)
(ii) 1 meter is slightly bigger than a yard, so multiply by 0.91 to make your number smaller.
1 yard = 1 × 0.91 m = 0.91 m
Solution continues…

12. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 3
Convert 1 yard into meters by:
(i) converting yards to inches, inches to centimeters, and then centimeters to meters,
(ii) using the conversion factor 0.91,
(iii) using the conversion factor 1.09.
Comment on your answers.
Solution (continued)
(iii) Divide by 1.09 to make the number bigger.
1 yard = 1 ÷ 1.09 m = … m
The three answers are slightly different. This is because the conversion factors used are only approximations.

13. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Guided Practice
Convert the following:
1. 6 meters to yards
2. 18 yards to meters
3. 3 feet to centimeters
4. 2 miles to meters
5. 2 kilometers to yards
6. 6 inches to millimeters
7. 9 yards to centimeters
8. 24 feet to dekameters
1 m = 1.09 yd, so 6 × 1.09 = 6.54 yards
1 yd = 0.91 m, so 18 × 0.91 = m
1 ft = cm, so 3 × = cm
1 mi = 1.61 km, so 2 × 1.61 = 3.22 km 1 km = 1000 m, so 3.22 × 1000 = 3220 m
1 km = 1000 m, so 2 × 1000 = 2000 m 1 m = 1.09 yd, so 2000 × 1.09 = 2180 yd
1 in = 2.54 cm, so 6 × 2.54 = cm 1 cm = 10 mm, so × 10 = mm
1 yd = 0.91 m, so 9 × 0.91 = 8.19 m 1 m = 100 cm, so 8.19 × 100 = 819 cm
1 ft = cm, so 24 × = cm 1 cm = dam, so × = dam
Solution follows…

14. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Guided Practice
9. Josh runs a marathon of 26 miles and 385 yards. How far is this in kilometers?
26 × = 46,145 yd
= 46,145 × 0.91 ÷ 1000 km = km (to 2 d.p.)
10. A boat race is 4 miles and 374 yards. How long is the race in meters?
4 × = 7414 yd
= 7414 × 0.91 m = m (to 2 d.p.)
Solution follows…

15. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
You Can Use Proportions Too
The examples so far have been done by reasoning whether to multiply or divide by the conversion factor.
But you could do them using proportions if you prefer.
Just use the numbers in the conversion tables as ratios.

16. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 4
Convert 10 km to miles.
Solution
This is the same as Example 1, but this time it’s done with proportions.
As always when using proportions, you need two ratios.
● The first ratio of miles to kilometers comes from the table:
1 : 1.61, or 1
1.61
● The second ratio involves the measurement you want to convert. Call the converted distance d miles. The ratio is:
d : 10, or d 10
Solution continues…
Solution follows…

17. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 4
Convert 10 km to miles.
Solution (continued)
Ratios:
and 1
1.61 d 10
Now write a proportion and solve by cross-multiplication: 1
1.61 d 10 =
1.61d = 10
Cross-multiply
d = 10 ÷ 1.61
Divide both sides by 1.61
d = 6.21 miles (to 2 decimal places)

18. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Guided Practice
Convert the following using proportions:
meters to yards
Call the converted distance x yd,
So, x = 10.9 yd. 1
1.09 10 x =
yards to meters
Call the converted distance x m,
So, x = 2.73 m. 1
0.91 3 x =
feet to centimeters
Call the converted distance x cm,
So, x = cm. 1
30.48
3.7 x =
miles to meters
Call the converted distance x m,
So, x = 8211 m. 1
1610
5.1 x =
Solution follows…

19. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Convert Weight and Time in Exactly the Same Way
So far, you’ve only looked at converting lengths.
But you can convert time and weight (and most other kinds of quantities) in exactly the same way.
You just need to know the conversion factor.

20. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Example 5
Convert 1 hour to seconds.
Solution
Do this in two stages — hours to minutes, and then minutes to seconds.
There are 60 minutes in an hour, and 60 seconds in a minute, so the conversion factor for both stages is 60.
1) Minutes are a smaller unit than hours, so multiply by 60 to get a bigger number: 1 hour = 1 × 60 = 60 minutes
2) Seconds are a smaller unit than minutes, so again multiply by 60: 60 minutes = 60 × 60 = 3600 seconds
Solution follows…

21. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Guided Practice
Use the information below to convert the quantities that follow.
1 kg = 2.2 lb, 1 gallon = 3.79 liters
15. 3 kg to lb
1 kg = 2.2 lb, so 3 × 2.2 = 6.6 lb
lb to kilograms
1 lb = (1 ÷ 2.2) kg = kg, so 16 × = 7.27 kg
17. 7 gallons to liters
1 gallon = 3.79 liters, so 7 × 3.79 = liters
liters to gallons
1 liter = (1 ÷ 3.79) gallons = gallons, so 44 × = gallons
Solution follows…

22. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Independent Practice
In Exercises 1–6, find the missing length. Give your answers to 2 decimal places.
in. = ? cm mm = ? in.
3. 14 yd = ? m m = ? in.
cm = ? yd ft = ? m
11.43
3.9
12.74
19.62
5.45
13.72
7. The length of a model plane is 56 inches. How long is the model in meters?
1.42 m (to 2 decimal places)
Solution follows…

23. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Independent Practice
8. Michaela and Ricky are each trying to guess how many feet are in a kilometer. Michaela guessed 3000 and Ricky guessed Whose guess was closest to the correct number of feet?
Actual answer is 3281 (to nearest whole number) so Ricky is (slightly) closer.
9. How many kilometers are there in 215,820 inches?
5.48 km (to 2 decimal places)
10. The dimensions of Zak’s bedroom are 5 ft × 8 ft. What are the dimensions of his room in meters?
1.52 m × 2.44 m (both to 2 decimal places)
Solution follows…

24. Converting Between Unit Systems
Lesson
4.3.3
Converting Between Unit Systems
Round Up
You’ve now seen how to convert between different unit systems of length.
And if you can do that, you can also convert pretty much anything else you want.
For example, you might want to convert dollars to some other currency if you travel overseas.