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Changing Metric Units
BEFORE
Now
WHY?
You learned metric units for
length, mass, and capacity.
You’ll change from one metric
unit of measure to another.
So you can find the height of a
sunflower in meters, as in Ex. 27.
Changing Units You can change from one unit to another in the
Word Watch
Review Words
meter, p. 56
gram, p. 187
liter, p. 188
metric system by multiplying or dividing by a power of 10.
Change to a larger unit by dividing.
1000
10
100
milli- centi- deci 10
1000
base unit (m, g, or L)
100
1000
deka- hecto- kilo 1000
Change to a smaller unit by multiplying.
EXAMPLE
1
Changing Units Using Multiplication
Change 0.64 L to milliliters.
Change to a smaller unit by multiplying.
1 Decide whether to multiply
or divide.
2 Select the power of 10.
1000
mL
L
0.64 1000 640.
ANSWER 0.64 L 640 mL
EXAMPLE
2
Changing Units Using Division
Change 23.6 g to kilograms.
1 Decide whether to multiply
or divide.
2 Select the power of 10.
Change to a larger unit by dividing.
1000
g
kg
23.6 1000 0.0236
ANSWER 23.6 g 0.0236 kg
Your turn now
Copy and complete the statement.
1. 230 g _?_ kg
2. 2.5 mL _?_ L
Lesson 4.8
3. 0.45 m _?_ cm
Changing Metric Units
191
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Comparing Measures To compare measures that have different
units, change one of them so that both measures have the same units.
EXAMPLE
with
Solving
3
Comparing Measures
Which is longer, 170 cm or 1.6 m?
You can change either unit
to the other. In Example 3,
you could have changed
1.6 meters to centimeters
instead.
Change 170 cm to meters so the units are the same for both measures.
170 cm (170 100) m
100 cm 1 m
1.7 m
Then compare the measures.
Because 1.7 m > 1.6 m, you know that 170 cm > 1.6 m.
ANSWER 170 cm is longer than 1.6 m.
Your turn now
Copy and complete the statement with <, >, or .
4. 50 mm _?_ 3.5 cm
EXAMPLE
4
5. 450 mL _?_ 5 L
6. 0.01 kg _?_ 10 g
Using a Verbal Model
State Quarters A bank filled with state quarters has a mass of 2.3 kg. The
bank’s mass is 0.9 kg when empty. Given that a quarter has a mass of
about 5.6 g, about how many quarters are in the bank?
Solution
1 Write a verbal model to
find the mass of the
quarters in the bank.
Mass of
Mass of
Mass of
quarters
full bank
empty bank
2.3 kg
1.4 kg
2 Change the mass of the
quarters to grams.
1.4 kg (1.4 1000) g
3 Find the number of quarters by
dividing the mass of the quarters
by the mass of one quarter.
250.
561
4
0
0
0
.
112
280
280
0
1400 g
ANSWER There are about 250 state quarters in the bank.
192
Chapter 4
0.9 kg
Decimal Multiplication and Division
Page 3 of 7
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Name the three base units for length, mass,
and capacity in the metric system.
2. To change from a smaller unit to a larger unit, do you multiply
or divide?
Copy and complete the statement.
3. 520 mg _?_ g
4. 360 cm _?_ m
5. 0.8 L _?_ mL
6. Guided Problem Solving You are comparing lemonade
mixes. Mix A will make four 2 liter pitchers of lemonade.
Mix B will make twenty 500 milliliter glasses of
lemonade. Which mix will make more lemonade?
1 Find the total number of liters of lemonade
Mix A makes.
2 Find the total number of milliliters of lemonade
Mix B makes.
3 Change the amount of lemonade Mix B makes to liters.
4 Compare the two amounts. Which mix will make more lemonade?
Practice and Problem Solving
Tell whether you would multiply or divide to change the units.
7. Change milliliters to liters.
8. Change grams to milligrams.
9. Change meters to centimeters.
10. Change grams to kilograms.
Copy and complete the statement.
with
Example
1
2
3
4
Homework
Exercises
7–27
7–27
28–35
36–39
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
11. To change from millimeters to centimeters, you divide by _?_.
12. To change from meters to kilometers, you divide by _?_.
13. To change from kilograms to grams, you multiply by _?_.
14. To change from liters to milliliters, you multiply by _?_.
Copy and complete the statement.
15. 8 mm _?_ cm
16. 0.04 L _?_ mL
17. 255 g _?_ kg
18. 6.25 g _?_ mg
19. 4 km _?_ m
20. 468 mL _?_ L
21. 0.8 kg _?_ g
22. 7.4 cm _?_ mm
23. 8.1 kL _?_ L
Lesson 4.8
Changing Metric Units
193
Page 4 of 7
24. How many grams are in 0.49 kilogram?
25. How many liters are in 750 milliliters?
26. Lions A grown male lion has a mass of about 180,000 grams.
What is the mass of the lion in kilograms?
27. Flowers A sunflower has a height of 64 centimeters. What is
the sunflower’s height in meters?
Copy and complete the statement with <, >, or .
28. 308 g _?_ 0.4 kg
29. 1.2 km _?_ 1300 m
30. 1.3 kL _?_ 1300 L
31. 70 mL _?_ 0.7 L
32. 34.8 kg _?_ 3480 g
33. 452 L _?_ 4600 mL
Animals Tell which dimension is greater.
34. A butterfly has a wingspan of 77 millimeters and a height of
7 centimeters. Which is greater, wingspan or height?
35. An orangutan has an arm span of 2.1 meters and a height of
140 centimeters. Which is greater, arm span or height?
Extended Problem Solving In Exercises 36–39, use the chart
showing the masses of 6 bowling balls.
36. What common unit of mass could you
use so that each mass is in the same unit?
37. Calculate Change the masses in the table
to the unit you chose in Exercise 36.
38. Compare List the masses in order from
least to greatest.
Bowling Balls
2.72 kg
7260 g
5,980,000 mg
2,720,000 mg
4.52 kg
6790 g
39. Decide Find the mean, median, and mode(s)
of the masses. Which averages best represent the data? Explain.
40. Critical Thinking Melissa and Jennifer each measure the width of a
standard piece of paper. Melissa says the paper is 216 mm wide.
Jennifer says the paper is 22 cm wide. Which measurement is more
accurate? Explain your reasoning.
Comparing Areas In Exercises 41 and 42, use a square with side
length 1.2 kilometers.
41. Find the area of the square in square kilometers.
42. Find the side length of the square in meters and its area in
square meters.
43. Based on your answers to Exercises 41 and 42, how do square
kilometers compare with square meters?
194
Chapter 4
Decimal Multiplication and Division
Page 5 of 7
Algebra Suppose x represents a length in meters. Tell whether the
expression represents the same length in the given unit.
45. (x 1000) km
44. (100x) cm
46. (x 1000) mm
47. Challenge Every centimeter on a map of your town represents an
actual distance of 200 meters. If you measure 8.5 centimeters on the
map, how many kilometers does it represent?
Mixed Review
Find the value of the power. (Lesson 1.3)
48. 33
49. 26
50. 10 squared
51. 4 cubed
Multiply. Use estimation to check that the product is reasonable.
(Lesson 4.3, 4.5)
52. 2.8 0.9
53. 0.5 4.8
56. 1000 3.492 57. 0.01 458.7
54. 7.318 5.1
55. 6.94 4.7
58. 0.01 64.76
59. 100 31.6
Basic Skills Order the numbers from least to greatest.
60. 64, 78, 29, 32
61. 105, 150, 101, 110
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
62. Extended Response A 591 milliliter container of juice costs $1.25. A
1.89 liter container of the same juice costs $3.29. Find the cost per liter
for each container of juice. Which container is the better buy? Explain
how you found your answer.
Fruit Punch
You want to make some fruit punch, but your little sister
has taken the measuring cup you need and she won’t tell
you where it is. You need to measure out 500 mL of water
for the punch.
If you have a pitcher for the fruit punch, an unmarked
300 mL container, and an unmarked 1 L container, how can
you measure out the right amount of water for the fruit punch?
Lesson 4.8
Changing Metric Units
195
Page 6 of 7
4.5 TO
4. 8
Notebook Review
Check Your Definitions
kilogram, p. 187
capacity, p. 188
liter, p. 188
mass, p. 187
gram, p. 187
milligram, p. 187
Review the
vocabulary
definitions in
your notebook.
Copy the review
examples in your
notebook. Then
complete the
exercises.
milliliter, p. 188
kiloliter, p. 188
Use Your Vocabulary
1. Copy and complete: The kilogram is a measure of _?_ while the milliliter
is a measure of _?_.
2. Writing Explain the first step needed to find the quotient 31.97 2.78.
4.5 Can you multiply and divide by powers of ten?
EXAMPLE Evaluate using mental math.
a. 1357.25 0.001 1.35725
Move decimal point 3 places to the left.
1.35725
b. 46.9 0.01 4690.
Move decimal point 2 places to the right.
4690
✓
Evaluate using mental math.
3. 38.06 10
4. 459.1 0.01 5. 621.37 10
6. 97.8 0.001
4.6 Can you divide by decimals?
EXAMPLE To divide 24 0.03, multiply the divisor and dividend by 100.
24 0.03
0.032
4
.0
0
800
4
0
0
32
2400
0
ANSWER 24 0.03 800
✓
Divide. Round to the nearest tenth if necessary.
7. 620 0.58
196
Chapter 4
8. 11.8 0.27
Decimal Multiplication and Division
9. 38 1.6
10. 303.2 0.5
Page 7 of 7
4.7 Can you use metric units of mass and capacity?
EXAMPLE Choose an appropriate metric unit to measure the mass of
a laptop computer.
ANSWER A kilogram is about the mass of this book and the mass of a
laptop computer would be at least the same as this book. So, kilograms
is an appropriate unit of measure for the mass of a laptop computer.
✓
Choose an appropriate metric unit to measure the item.
11. mass of a mouse
12. capacity of a coffee cup
4.8 Can you change metric units?
EXAMPLE Copy and complete the statement.
a. 52 g _?_ mg
✓
b. 36.8 mL _?_ L
52 1000 52,000
36.8 1000 0.0368
ANSWER 52 g 52,000 mg
ANSWER 36.8 mL 0.0368 L
Copy and complete the statement.
13. 24.5 L _?_ kL
14. 21.2 kg _?_ g
15. 20 mm _?_ cm
about Lessons 4.5–4.8
16. Writing How do you change from a smaller metric unit to a larger
metric unit? How do you change from a larger to a smaller unit?
Review Quiz 2
Find the product or quotient. Use mental math, if possible.
1. 4.56 100
2. 9.75 0.01
3. 27.9 0.09
4. 135 2.5
5. 61.4 0.04
6. 36 1.8
7. 50.8 0.5
8. 0.748 0.22
9. Is the capacity of a backpack measured in liters or milliliters?
Copy and complete the statement.
10. 10 L _?_ mL
11. 7 cm _?_ m
Lessons 4.5–4.8
12. 5.02 g _?_ kg
Notebook Review
197