SECTION 2.4
Place Value, Rounding, and Estimations 63
2.4 PLACE VALUE, ROUNDING, AND ESTIMATIONS
Textbook Reference Section 4.2
CLAST OBJECTIVES
" Recognize the role of the base number in the base – ten numeration system
" Identify a reasonable estimate of sum, average, or product
10 5
10 4
10 3
10 2
10 1
on
es
(de
cim
a
ten l po
int
th
)
hu
nd
red
ten th
tho
hu usan
nd
d
red th
tho
us
an
dth
hu
nd
red
ten tho
tho usa
n
tho usan ds
d
us
an s
d
s
hu
nd
red
ten s
s
Place Value
10 0
•••
1
10 1
.
1
1
10 2 10 3
1
10 4
•••
The place value of any digit can be found by following the format in the chart above.
Examples
a) What is the place value of 8 in 5.3897?
Solutions
The 8 is two places right of the decimal
1
point. Thus, the place value of 8 is
.
10 2
b) What is the place value of 4 in 7,493.32?
The 4 is three places left of the decimal
point. Thus, the place value of 4 is 10 2.
c) Write the expanded form of 407.02.
Consider the place values of the 4, 7, and 2.
⎛
1 ⎞⎟
2
0
4 × 10
+ 7 × 10
+ ⎜2 ×
2
⎜
10 ⎟⎠
⎝
(
d) Write the numeral for
1⎞
⎛
2 × 10 3 + (3 × 10 ) + ⎜ 5 × ⎟
⎝ 10 ⎠
(
)
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) (
)
2 is four places left of the decimal point.
3 is two places left of the decimal point.
5 is one place right of the decimal point.
2__3__.5
Place zeroes in the hundreds place and the
ones place.
Result: 2030.5
64 CHAPTER 2
Arithmetic
Check Your Progress 2.4
For Questions 1 – 4, give the place value of the underlined digit.
1. 8,394.5126
2. 8,394.5126
3. 8,394.5126
4. 8,394.5126
For Questions 5 – 7, write the numeral in expanded form.
5. 24.38
6. 7,040.09
7. 508.4
For Questions 8 – 10, write the numeral.
1⎞
⎛
8. 1 × 10 2 + 5 × 10 0 + ⎜ 7 × ⎟
⎝ 10 ⎠
(
) (
9.
(
9 × 10
10.
(
4 × 10
4
0
)
)+ (
2 × 10
) + ⎛⎜ 9 ×
⎝
2
) + ⎛⎜1 ×
⎝
1 ⎞
⎟
10 2 ⎠
1 ⎞ ⎛
1 ⎞
+ ⎜7 ×
⎟
2 ⎟
10 ⎠ ⎝ 10 3 ⎠
Rounding
Note the digit x that is specified.
• If the digit after x is 5 or greater than 5, increase x by one and replace all the digits
after x with zeroes.
• If the digit after x is less than 5, leave x as it is and replace all the digits after x with
zeroes.
• Note that some zeroes will be insignificant.
Examples
e) Round 73.159 to the nearest tenth.
Solutions
The 1 is in the tenth place. The digit after 1
is 5, so increase 1 to 2.
Result: 73.200 or 73.2
f) Round 73.159 to the nearest one.
The 3 is in the ones place. The digit after 3
is 1 which is less than 5, so do not increase 3.
Result: 73.000 or 73
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SECTION 2.4
Place Value, Rounding, and Estimations 65
Check Your Progress 2.4
11. Round 8,490.372 to the nearest hundredth.
12. Round 8,492.372 to the nearest one.
13. Round 8,490.372 to the nearest hundred.
14. Round 8,490.372 to the nearest tenth.
Estimation: A rough calculation using rounded numbers.
Examples
g) Gas is sold at $1.89 a gallon and Tom’s
car takes 19 gallons. What is a reasonable
estimate of Tom’s gas bill?
Solutions
Round $1.89 to $2.00
Round 19 gallons to 20 gallons
Estimate: ($2)(20) = $40
h) Jenny bought perfume for $12.99, nail
polish for $3.15, lipstick for $7.95, and
earrings for $7.19. About how much money
did Jenny spend?
Round $12.99 to $13.00
Round $3.15 to $3.00
Round $7.95 to $8.00
Round $7.19 to $7.00
Estimate: $13 + $3 + $8 + $7 = $31
i) Three hundred students took an English
examination. All of the students scored less
than 93, but more than 61. What is a
reasonable estimate of the average score of
the students?
j) A music store has 30 employees. The
largest gross pay is $300 per week, and the
lowest is $200 per week. Estimate the
weekly payroll at the music store.
Estimate:
93 + 61 154
=
= 77
2
2
Average pay:
300 + 200 500
=
= 250
2
2
Estimate: 30($250) = $7,500
Check Your Progress 2.4
15. Bill owns 432.87 shares of a mutual fund valued at $40.17 per share. Find a
reasonable estimate of the value of Bill’s stock to the nearest hundred dollars.
16. A unit of water costs $2.09 and 60.34 units are used. Find a reasonable estimate of
the bill to the nearest hundred dollars.
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66 CHAPTER 2
Arithmetic
17. Seventy students took a test. If the highest score was 96 and the lowest score was 72,
what was the class average.
18. On a certain day, the college cafeteria sold 70 lunch specials. The lowest special was
$3 and the highest was $7. What is the estimate of income from lunch specials that day?
19. A bag of fertilizer covers 1.75 acres. What is a reasonable estimate of the number of
acres that could be covered with 159.5 bags of fertilizer?
20. Below are the prices of the four most active stocks on a certain Exchange and their
closing prices per share in dollar.
Tallar Corp
Paxin Inc
Fun NY
Aninus
5
8
3
3
4
1
4
2
1
14
3
11
What would be a reasonable estimate of the average closing price per share for these
stocks?
See If You
Remember
1. 349.248 + 2.9 + 51.73
3. 4
2 ⎛
− ⎜−
5 ⎝
1⎞
⎟
7⎠
SECTIONS 2.1 – 2.3
2. (22.8)(1.4)
4. − 2
1 ⎛ 3⎞
÷ ⎜− ⎟
4 ⎝ 5⎠
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SECTION 2.4
Place Value, Rounding, and Estimations 67
5. Change 0.25 % to decimal.
6. Change
7
to decimal.
8
7. Write 0.655 as a fraction.
8. 18 is 30 % of what number?
9. 7 is what percent of 35?
10. If 32 is decreased to 24, what is the percent decrease?
11. If you increase 60 by 150 %, what is the result?
12. Peter weighed 160 pounds. After the vacation, his weight increased by 20 %. What is
his new weight?
13. A car that originally cost $25,000.00 has now depreciated by 10%. What is the
present value of the car?
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