Page 1 of 4
Comparing, Ordering, and
Rounding Decimals
BEFORE
Now
WHY?
You compared, ordered, and
rounded whole numbers.
You’ll compare, order, and
round decimals.
So you can order soapbox derby
times, as in Ex. 34.
In the Real World
Word Watch
decimal, p. 52
Olympic Games In the 1968 Summer Olympics, Irena Szewinska of
Poland won the women’s 200 meter dash with a time of 22.5 seconds.
In 1996, Marie-Jose Perec of France won the event with a time of
22.12 seconds. Whose time is faster?
The numbers 22.5 and 22.12 are decimals. A decimal is a number that is
written using the base-ten place value system where a decimal point
separates the ones’ and tenths’ digits. Each place value is 10 times the
place value to its right.
hu
nd
ten red
t th
tho hou ous
us san and
hu an ds s
nd ds
ten red
s s
on
es
ten
th
hu s
nd
tho red
u th
ten san s
- dt
hu thou hs
nd sa
red nd
-th ths
ou
sa
nd
ths
Decimals and Place Value
2 2•5
2 2•1 2
twenty-two and five tenths
twenty-two and twelve
hundredths
To compare decimals, write the numbers in a column, lining up the
decimal points. If needed, write zeros as placeholders so that all decimals
have the same number of digits. Then compare digits from left to right.
EXAMPLE
1
Comparing Decimals
To determine whose time is faster, compare 22.5 and 22.12.
The tens’ and ones’ digits are the same.
22.50
22.12
Write a zero as a placeholder.
The tenths’ digits are different. 5 > 1, so 22.50 > 22.12.
ANSWER Because 22.5 > 22.12, Perec’s time is faster.
Marie-Jose Perec
52
Chapter 2
Decimal Operations
Page 2 of 4
Your turn now
Copy and complete the statement using <, >, or .
1. 20.05 _?_ 20.1
EXAMPLE
2
2. 7.7 _?_ 7.70
3. 5.701 _?_ 5.699
Ordering Decimals
Order 2.11, 2.21, 2, 2.06, and 2.24 from least to greatest.
with
Solving
Remember that numbers
on a number line increase
from left to right.
On a number line, mark tenths between 2.0 and 2.3. Mark hundredths by
dividing each tenth into ten equal parts. Then graph each number.
2
2.06
2.0
2.11
2.21
2.1
2.24
2.2
2.3
ANSWER From least to greatest, the numbers are 2, 2.06, 2.11, 2.21, and 2.24.
Rounding Decimals
To round a decimal to a given place value, look at the digit in
the place to the right.
• If the digit is less than 5, round down.
• If the digit is 5 or greater, round up.
EXAMPLE
3
Rounding a Decimal
Round 7.126 to the nearest tenth.
You want to round to the nearest tenth.
7.126
Because the hundredths’ digit is less than 5,
round down and drop the remaining digits.
ANSWER The decimal 7.126 rounded to the nearest tenth is 7.1.
Your turn now
Order the numbers from least to greatest.
4. 3.84, 4.4, 4.83, 3.48, 4.38
5. 5.71, 5.8, 5.68, 5.79, 5.6
6. Round 34.0152 to the nearest hundredth.
Lesson 2.1
Comparing, Ordering, and Rounding Decimals
53
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 706
Getting Ready to Practice
Vocabulary Match the number with the place value of the red digit.
1. 27.404
2. 3.579
3. 4.128
4. 15.26
A. ones
B. tenths
C. hundredths
D. thousandths
5. Name the numbers represented by the labeled points on the
number line.
A
B
C
5.2
5.3
D
E
5.4
5.5
Copy and complete the statement using <, >, or .
6. 6.5 _?_ 6.45
7. 12.8 _?_ 12.801
8. 30.650 _?_ 30.65
Round 21.6804 to the specified place value.
9. ones
10. tenths
13. Earthquakes Moment
magnitude is a measure used
by scientists to describe an
earthquake’s power. Order
the moment magnitudes
from least to greatest.
Map showing an
earthquake fault
11. hundredths
12. thousandths
Earthquake
Location
Year
Moment
Magnitude
Ecuador
1906
8.8
Chile
1960
9.5
Alaska, U.S.
1965
8.7
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
18–27
28–34
35–42
Online Resources
Match the decimal with its verbal description.
14. 7.086
A. Seven and eighty-six hundredths
15. 7.86
B. Seventy and eighty-six hundredths
16. 78.06
C. Seventy-eight and six hundredths
17. 70.86
D. Seven and eighty-six thousandths
CLASSZONE.COM
• More Examples
• eTutorial Plus
54
Chapter 2
Copy and complete the statement using <, >, or .
18. 3.2 _?_ 2.3
19. 7.08 _?_ 7.03
20. 0.19 _?_ 0.20
21. 8.49 _?_ 8.48
22. 10.01 _?_ 10.10
23. 0.8 _?_ 1.3
24. 13.20 _?_ 13.2
25. 0.607 _?_ 0.66
26. 25.024 _?_ 26.023
Decimal Operations
Page 4 of 4
27. Tents You and a friend are taking an overnight backpacking trip. You
are both carrying lightweight tents. Your tent weighs 3.5 pounds, and
your friend’s tent weighs 3.25 pounds. Whose tent weighs less?
Sports
Order the numbers from least to greatest.
28. 1.2, 3.2, 0.2, 0.9
29. 6.6, 6.2, 6.8, 6.5
30. 2.2, 1.1, 2.01, 1.02
31. 0.86, 0.03, 0.91, 0.2 32. 4.3, 4.03, 4.27, 4.23 33. 8.56, 7.65, 8.65, 7.63
34. Soapbox Derby The winning times in each division for a soapbox
derby are 29.15 seconds, 29.78 seconds, and 29.74 seconds. Order
the times from fastest to slowest.
Round the decimal as specified.
■
Soapbox Derby
A soapbox derby is a
downhill competition in which
kids race homemade cars.
If 3 cars race at a time, and
84 cars are entered in the
derby, how many groups of
3 cars must there be?
35. 17.6 (nearest one)
36. 32.09 (nearest tenth)
37. 5.55 (nearest tenth)
38. 12.0092 (nearest thousandth)
39. 2.2949 (nearest hundredth)
40. 0.73 (nearest one)
41. 0.009 (nearest tenth)
42. 9.9999 (nearest hundredth)
43. Critical Thinking Write two numbers that round to 5.7.
Describe the pattern. Then write the next two numbers.
44. 10, 1, 0.1, 0.01, . . .
45. 2.01, 2.002, 2.0003, 2.00004, . . .
46. Challenge Write two numbers that are between 4.57 and 4.59.
Mixed Review
Evaluate the expression. (Lesson 1.4)
48. 4 p 2 p 32
47. 5 12 2
49. 52 12 p 3
50. One box of candy holds 50 pieces. How many boxes of candy do you
need to make 16 goodie bags, each with 12 pieces of candy? (Lesson 1.7)
Basic Skills Estimate the sum.
51. 39 71 57
52. 427 262 105
53. 962 105 890
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
54. Multiple Choice Which statement is true?
A. 4.59 < 4.5
B. 7.41 > 7.401
C. 1.09 < 1.081
D. 6.33 > 6.333
55. Short Response Explain in words how to round 19.967 to the nearest
tenth.
Lesson 2.1
Comparing, Ordering, and Rounding Decimals
55