6-5 Measurement:

Changing Metric Units

MAIN IDEA
Change metric units of
The lengths of two objects are shown below.
length, capacity, and
mass. Length Length
Object
(millimeters) (centimeters)
New Vocabulary paper clip 45 4.5
metric system CD case 144 14.4
meter
liter
1. Select three other objects. Find and record the width of all five
gram
kilogram objects to the nearest millimeter and tenth of a centimeter.
2. Compare the measurements of the objects, and write a rule that
Math Online describes how to convert from millimeters to centimeters.
glencoe.com 3. Measure the length of your classroom in meters. Make a
• Extra Examples conjecture about how to convert this measure to centimeters.
• Personal Tutor
• Self-Check Quiz Explain. 1–3. See margin.

The metric system is a decimal system of measures. The prefixes

commonly used in this system are kilo-, centi-, and milli-.

Meaning Meaning
Prefix
In Words In Numbers
kilo- thousands 1,000
centi- hundredths 0.01
milli- thousandths 0.001

In the metric system, the base unit of length is the meter (m). Using the
prefixes, the names of other units of length are formed. Notice that the
prefixes tell you how the units relate to the meter.

Unit Symbol Relationship to Meter

kilometer km 1 km = 1,000 m 1 m = 0.001 km
meter m 1m=1m
centimeter cm 1 cm = 0.01 m 1 m = 100 cm
millimeter mm 1 mm = 0.001 m 1 m = 1,000 mm

The liter (L) is the base unit of capacity, the amount of dry or liquid
material an object can hold. The gram (g) measures mass, the amount
of matter in an object. The prefixes can also be applied to these units.
Whereas the meter and liter are the base units of length and capacity,
the base unit of mass is the kilogram (kg).

304 Chapter 6 Ratios and Proportions

 To change a metric measure of length, mass, or capacity from one unit
to another, you can use the relationship between the two units and
multiplication by a power of 10.

Convert Units in the Metric System

1 Convert 4.5 liters to milliliters.
Metric Conversions You need to convert liters to milliliters. Use the relationship
When converting from a 1 L = 1,000 mL.
larger unit to a smaller
unit, the power of ten 1 L = 1,000 mL Write the relationship.
being multiplied will be
greater than 1. 4.5 × 1 L = 4.5 × 1,000 mL Multiply each side by 4.5 since
When converting from a you have 4.5 L.
smaller unit to a larger 4.5 L = 4,500 mL To multiply 4.5 by 1,000, move the
unit, the power of ten will decimal point 3 places to the right.
be less than 1.
2 Convert 500 millimeters to meters.
You need to convert millimeters to meters. Use the relationship
1 mm = 0.001 m.
1 mm = 0.001 m Write the relationship.
500 × 1 mm = 500 × 0.001 m Multiply each side by 500 since
you have 500 mm.
500 mm = 0.5 m To multiply 500 by 0.001, move the
decimal point 3 places to the left.

Complete.
a. 25.4 g = kg 0.0254 b. 158 mm = m 0.158

3 BEARS The California Grizzly Bear was designated the official state
animal in 1953. Use the information at the left to find the maximum
weight of a grizzly bear in grams.
You are converting kilograms to grams. Since the maximum weight of
a grizzly bear is 521.64 kilograms, use the relationship 1 kg = 1,000 g.
1 kg = 1,000 g Write the relationship.

521.64 × 1 kg = 521.64 × 1,000 g Multiply each side by 521.64

since you have 521.64 kg.
521.64 kg = 521,640 g To multiply 521.64 by 1,000, move
Real-World Link the decimal point 3 places to the right.
The maximum weight So, the maximum weight of a grizzly bear is 521,640 grams.
of a grizzly bear is
521.64 kilograms.
Source: North American Bear Center

c. FOOD A bottle contains 1.75 liters of juice. How many milliliters

is this? 1,750 mL

Lesson 6-5 Measurement: Changing Metric Units 305

 To convert measures between customary units and metric units, use
the relationships below.

Customary and Metric Relationships Key Concept

Type of Measure Customary Metric

Length 1 inch (in.) ≈ 2.54 centimeters (cm)

1 foot (ft) ≈ 0.30 meter (m)
1 yard (yd) ≈ 0.91 meter (m)
1 mile (mi) ≈ 1.61 kilometers (km)

Weight/Mass 1 pound (lb) ≈ 453.6 grams (g)

1 pound (lb) ≈ 0.4536 kilogram (kg)
1 ton (T) ≈ 907.2 kilograms (kg)

Capacity 1 cup (c) ≈ 236.59 milliliters (mL)

1 pint (pt) ≈ 473.18 milliliters (mL)
1 quart (qt) ≈ 946.35 milliliters (mL)
1 gallon (gal) ≈ 3.79 liters (L)

Convert Between Measurement Systems

4 Convert 17.22 inches to centimeters. Round to the nearest
hundredth if necessary.

Alternative Method Use the relationship 1 inch ≈ 2.54 centimeters.

When converting 17.22
inches to centimeters, you 1 inch ≈ 2.54 cm Write the relationship.
can use the relationship
1 in. ≈ 2.54 cm or the 17.22 × 1 in. ≈ 17.22 × 2.54 cm Multiply each side by 17.22 since
unit ratio _2.54 cm
. you have 17.22 in.
1 in.
17.22 in. ≈ 43.7388 cm Simplify.

So, 17.22 inches is approximately 43.74 centimeters.

5 Convert 828.5 milliliters to cups. Round to the nearest hundredth

if necessary.
Since 1 cup ≈ 236.59 milliliters, multiply by _
1c
.
236.59 mL
828.5 mL ≈ 828.5 mL · _
1c
Multiply by _ .
1c
236.59 mL
236.59 mL
≈_
828.5 c
or 3.5 c Simplify.
236.59
So, 828.5 milliliters is approximately 3.5 cups.

Complete. Round to the nearest hundredth if necessary.

d. 1,760.23 d. 7.44 c ≈ mL e. 22.09 lb ≈ kg f. 35.85 L ≈ gal 9.46
e. 10.02

306 Chapter 6 Ratios and Proportions

 Convert with Rates
6 LIGHT The speed of light is about 186,000 miles per second.
Find the approximate speed of light in kilometers per second.
Since 1 mile ≈ 1.61 kilometers, multiply by _
1.61 km
.
1 mi
186,000 mi
_ 186,000 mi
s ≈_×_ 1.61 km
Multiply by _.
1.61 km
1s 1 mi 1 mi
299,460 km
≈_ Simplify.
1s
Real-World Link
So, the speed of light is approximately 299,460 kilometers per second.
Before the seventeenth
century, people thought
light was transmitted
instantly. Now, we
know that light is too g. RUNNING Chuck runs at a speed of 3 meters per second. About how
fast for the delay to be
noticeable. many feet per second does Chuck run? about 9.84 feet per second
Source: University of California,
Riverside
★ indicates multi-step problem

Examples 1, 2, 4, 5 Complete. Round to the nearest hundredth if necessary.

(pp. 305–306)
1. 3.7 m = cm 370 2. 550 m = km 0.55
3. 1,460 mg = g 1.46 4. 2.34 kL = L 2,340
5. 9.36 yd ≈ m 8.52 6. 11.07 pt ≈ mL 5,238.10
7. 58.14 kg ≈ lb 128.17 8. 38.44 cm ≈ in. 15.13

Examples 3, 6 9. SPORTS About how many feet does a team of athletes run in a
(pp. 305, 307) 1,600-meter relay race? about 5,333.33 ft

Complete. Round to the nearest hundredth if necessary.

HOMEWORK HELP
For See 10. 720 cm = m 7.2 11. 983 mm = m 0.98
Exercises Examples
12. 3.2 m = cm 320 13. 0.03 g = mg 30
10–23 1, 2, 4, 5
14. 997 g = kg 1.00 15. 82.1 g = kg 0.08
24–27 3, 6
16. 9.1 L = mL 9,100 17. 130.5 kL = L 130,500
Exercise Levels
18. 3.75 c ≈ mL 887.21 19. 41.8 in. ≈ cm 106.17
A: 10–27
B: 28–38 20. 156.25 lb ≈ kg 70.88 21. 9.5 gal ≈ L 36.01
C: 39–43 22. 680.4 g ≈ lb 1.5 23. 4.725 m ≈ ft 15.75

24. WATERFALLS At 979 meters tall, Angel Falls in Venezuela is the highest
waterfall in the world. How many kilometers tall is the waterfall? 0.979 km

25. FOOD An 18-ounce jar contains 510 grams of grape jelly. How many
kilograms of grape jelly does the jar contain? 0.51 kg

Lesson 6-5 Measurement: Changing Metric Units 307

 26. CYCLING Ramon rides his bike at a rate of 8 kilometers per hour. About how
many miles per hour can Ramon ride his bike? about 4.97 miles per hour

★ 27. BIRDS A gull can fly at a speed of 22 miles per hour. About how many
meters per hour can a gull fly? about 35,420 meters per hour

Complete. Round to the nearest hundredth if necessary.

28. 8.18 qt ≈ L 7.74 29. 15.09 km ≈ yd 16,582.42
30. 72.26 cm ≈ ft 2.37 31. 0.445 T ≈ g 403,704
32. 0.02 km, 3,000 cm, 50 m
Order each set of measures from least to greatest.
33. 0.06 L, 660 mL, 6.6 kL
32. 0.02 km, 50 m, 3,000 cm 33. 660 mL, 0.06 L, 6.6 kL
34. 0.32 kg, 345 g, 35,100 mg 35. 2,650 mm, 130 cm, 5 m
35,100 mg, 0.32 kg, 345 g 130 cm, 2650 mm, 5 m
36. ANALYZE TABLES The table shows the Bridge Length (m)
Real-World Link ★ lengths of bridges in the United States.
The Mackinac Bridge Mackinac, MI 1,158
opened on Which bridges are about 1 kilometer in
George Washington, NY 1,067
November 1, 1957. length? Justify your answer. See margin.
It is the longest Tacoma Narrows II, WA 853
two-tower suspension
Oakland Bay, CA 704
bridge between bases ★ 37. CARPENTRY Jacinta needs a 2.5-meter
in the Western Pennybacker, TX 345
Hemisphere. pole for a birdfeeder that she is building.
Sunshine Skyway, FL 8,712
Source: Encyclopaedia Britannica How many centimeters will she need to
cut off a 3-meter pole in order to use it Golden Gate, CA 2,780
for the birdfeeder? 50 cm
EXTRA PRACTICE 38. BAKING A bakery uses 900 grams of peaches per cobbler. How many
See pages 683, 709. ★ cobblers can be made using 10.5 pounds of peaches? 5 cobblers

H.O.T. Problems ★ 39. FIND THE ERROR Jake and Gerardo are converting 3.25 kilograms to grams.
Who is correct? Explain your reasoning.
39. Jake; Gerardo
divided 3.25 by
1,000. He should 3.25 kg = 3,250 g
have multiplied.

3.25 kg = 0.00325 g

Jake Gerardo
CHALLENGE For Exercises 40–42, use the following information.
The metric prefix giga refers to something one billion times larger than
the base unit.
40. How many meters are in one gigameter? 1,000,000,000 m
41. About how many miles are in one gigameter? Round to the nearest
hundredth. about 621,118.01 mi
42. about 149.73 gm 42. The distance from Earth to the Sun is approximately 93 million miles.
About how many gigameters is this? Round to the nearest hundredth.

308 Chapter 6 Ratios and Proportions

 43. WR ITING IN MATH Explain why it makes sense to multiply by a
power of 10 that is greater than 1 when changing from a larger unit
to a smaller unit. There are a greater number of smaller units.

44. The table shows the mass of four 45. Which relationship between the given
wireless telephones. Find the units of measure is correct? H
approximate total mass of the
F One gram is _
1
of a centigram.
telephones in kilograms. A 100

Telephone Owner Mass (g) G One meter is _

1
of a centimeter.
100
Elena 100.4
Kevin 70.8 H One gram is _
1
of a kilogram.
Marissa 95.6 1,000
Corey 120.4 J One milliliter is _1
of a liter.
100
A 0.39 kilogram
B 3.9 kilograms
C 39.0 kilograms
D 390.0 kilograms

46. MEASUREMENT A certain car weighs 3,200 pounds. What is the weight
of the car in tons? (Lesson 6-4) 1.6 T

47. MEASUREMENT The table shows the number of inches per foot. Graph the
data. Then find the slope of the line. Explain what slope represents.
(Lesson 6-3) See margin for graph. Slope:
1 _
; there are 12 inches in every foot.
12
Feet (x) 1 2 3 4
Inches (y) 12 24 36 48

Add or subtract. Write in simplest form. (Lesson 5-3)

48. 3_ + 1_ 4
4 1 5 _ 49. 8_ - 2_ 6
3 2 1 _ 50. 9_ + 4_
1 3 _
13 13 51. 11_ - 5_
7 3 19
5 _
7 7 7 5 5 5 6 8 24 10 4 20
52. BASKETBALL Jared made thirty-seven percent of his free-throw attempts
during basketball practice. Write this percent as a decimal. (Lesson 4-7) 0.37

PREREQUISITE SKILL Solve each equation. (Lesson 3-3)

53. 5 · 4 = x · 2 10 54. 9 · 24 = 27 · x 8 55. x · 15 = 12 · 4 3.2 56. 8_

1
· x = 11 · 17 22
2

Lesson 6-5 Measurement: Changing Metric Units 309