OpenStax-CNX module: m34959
1
Decimals: Rounding Decimals
∗
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This
module discusses how to round decimals. By the end of the module students should be able to round a
decimal number to a specied position.
1 Section Overview
• Rounding Decimal Numbers
2 Rounding Decimal Numbers
We rst considered the concept of rounding numbers in here1 where our concern with rounding was related
to whole numbers only. With a few minor changes, we can apply the same rules of rounding to decimals.
To round a decimal to a particular position:
1. Mark the position of the round-o digit (with an arrow or check).
2. Note whether the digit to the immediate right of the marked digit is
(a) less than 5. If so, leave the round-o digit unchanged.
(b) 5 or greater. If so, add 1 to the round-o digit.
3. If the round-o digit is
(a) to the right of the decimal point, eliminate all the digits to its right.
(b) to the left of the decimal point, replace all the digits between it and the decimal point with zeros
and eliminate the decimal point and all the decimal digits.
2.1 Sample Set A
Round each decimal to the specied position. (The numbers in parentheses indicate which step is being
used.)
Example 1
Round 32.116 to the nearest hundredth.
∗ Version
1.2: Aug 18, 2010 8:21 pm -0500
† http://creativecommons.org/licenses/by/3.0/
1 "Addition and Subtraction of Whole Numbers: Rounding Whole Numbers" <http://cnx.org/content/m34780/latest/>
http://cnx.org/content/m34959/1.2/
OpenStax-CNX module: m34959
(1)
(2b)
(3a)
2
The digit immediately to the right is 6, and 6 > 5, so we add 1 to the round-o digit:
1+1=2
The round-o digit is to the right of the decimal point, so we eliminate all digits to its right.
32.12
The number 32.116 rounded to the nearest hundredth is 32.12.
Example 2
Round 633.14216 to the nearest hundred.
(1)
(2a)
(3b)
The digit immediately to the right is 3, and 3 < 5 so we leave the round-o digit unchanged.
The round-o digit is to the left of 0, so we replace all the digits between it and the decimal
point with zeros and eliminate the decimal point and all the decimal digits. 600
The number 633.14216 rounded to the nearest hundred is 600.
Example 3
1,729.63 rounded to the nearest ten is 1,730.
Example 4
1.0144 rounded to the nearest tenth is 1.0.
Example 5
60.98 rounded to the nearest one is 61.
Sometimes we hear a phrase such as "round to three decimal places." This phrase means that the round-o
digit is the third decimal digit (the digit in the thousandths position).
Example 6
67.129 rounded to the second decimal place is 67.13.
Example 7
67.129558 rounded to 3 decimal places is 67.130.
2.2 Practice Set A
Round each decimal to the specied position.
Exercise 1
(Solution on p. 7.)
Exercise 2
(Solution on p. 7.)
Exercise 3
(Solution on p. 7.)
Exercise 4
(Solution on p. 7.)
Exercise 5
(Solution on p. 7.)
4.816 to the nearest hundredth.
0.35928 to the nearest ten thousandths.
82.1 to the nearest one.
753.98 to the nearest hundred.
Round 43.99446 to three decimal places.
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Exercise 6
(Solution on p. 7.)
Exercise 7
(Solution on p. 7.)
Round 105.019997 to four decimal places.
Round 99.9999 to two decimal places.
3 Exercises
For the rst 10 problems, complete the chart by rounding each decimal to the indicated positions.
Exercise 8
(Solution on p. 7.)
20.01071
Tenth
Hundredth
Thousandth
Ten Thousandth
Table 1
Exercise 9
3.52612
Tenth
Hundredth
3.53
Thousandth
Ten Thousandth
Table 2
Exercise 10
(Solution on p. 7.)
531.21878
Tenth
Hundredth
Thousandth
Ten Thousandth
Table 3
Exercise 11
36.109053
Tenth
36.1
Hundredth
Thousandth
Ten Thousandth
Table 4
Exercise 12
(Solution on p. 7.)
1.999994
Tenth
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Hundredth
Thousandth
Ten Thousandth
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4
Table 5
Exercise 13
7.4141998
Tenth
Hundredth
Thousandth
7.414
Ten Thousandth
Table 6
Exercise 14
(Solution on p. 7.)
0.000007
Tenth
Hundredth
Thousandth
Ten Thousandth
Table 7
Exercise 15
0.00008
Tenth
Hundredth
Thousandth
Ten Thousandth
0.0001
Table 8
Exercise 16
(Solution on p. 8.)
9.19191919
Tenth
Hundredth
Thousandth
Ten Thousandth
Table 9
Exercise 17
0.0876543
Tenth
Hundredth
Thousandth
Table 10
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Ten Thousandth
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Calculator Problems
For the following 5 problems, round 18.4168095 to the indicated place.
Exercise 18
(Solution on p. 8.)
3 decimal places.
Exercise 19
1 decimal place.
Exercise 20
(Solution on p. 8.)
5 decimal places.
Exercise 21
6 decimal places.
Exercise 22
(Solution on p. 8.)
2 decimal places.
Calculator Problems
For the following problems, perform each division using a calculator.
Exercise 23
4 ÷ 3 and round to 2 decimal places.
Exercise 24
1 ÷ 8 and round to 1 decimal place.
(Solution on p. 8.)
Exercise 25
1 ÷ 27 and round to 6 decimal places.
Exercise 26
51 ÷ 61 and round to 5 decimal places.
(Solution on p. 8.)
Exercise 27
3 ÷ 16 and round to 3 decimal places.
Exercise 28
16 ÷ 3 and round to 3 decimal places.
(Solution on p. 8.)
Exercise 29
26 ÷ 7 and round to 5 decimal places.
3.1 Exercises for Review
Exercise 30
( here2 ) What is the value of 2 in the number 421,916,017?
(Solution on p. 8.)
Exercise 31
( here3 ) Perform the division: 378 ÷ 29.
Exercise 32
( here4 ) Find the value of 44 .
Exercise 33
( here5 ) Convert
11
3
(Solution on p. 8.)
to a mixed number.
2 "Addition and Subtraction of Whole Numbers: Whole Numbers" <http://cnx.org/content/m34795/latest/>
3 "Multiplication and Division of Whole Numbers: Division of Whole Numbers" <http://cnx.org/content/m34865/latest/>
4 "Exponents, Roots, and Factorization of Whole Numbers: Exponents and Roots"
<http://cnx.org/content/m34871/latest/>
5 "Introduction to Fractions and Multiplication and Division of Fractions: Proper Fractions, Improper Fractions, and Mixed
Numbers" <http://cnx.org/content/m34912/latest/>
http://cnx.org/content/m34959/1.2/
OpenStax-CNX module: m34959
Exercise 34
( here6 ) Convert 3.16 to a mixed number fraction.
6 "Decimals: Converting a Decimal to a Fraction" <http://cnx.org/content/m34958/latest/>
http://cnx.org/content/m34959/1.2/
6
(Solution on p. 8.)
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Solutions to Exercises in this Module
Solution to Exercise (p. 2)
4.82
Solution to Exercise (p. 2)
0.3593
Solution to Exercise (p. 2)
82
Solution to Exercise (p. 2)
800
Solution to Exercise (p. 2)
43.994
Solution to Exercise (p. 3)
105.0200
Solution to Exercise (p. 3)
100.00
Solution to Exercise (p. 3)
Tenth
20.0
Hundredth
20.01
Thousandth
20.011
Ten Thousandth
20.0107
Table 11
Solution to Exercise (p. 3)
Tenth
531.2
Hundredth
531.22
Thousandth
531.219
Ten Thousandth
531.2188
Table 12
Solution to Exercise (p. 3)
Tenth
2.0
Hundredth
2.00
Thousandth
2.000
Ten Thousandth
2.0000
Table 13
Solution to Exercise (p. 4)
Tenth
0.0
Hundredth
0.00
Thousandth
0.000
Table 14
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Ten Thousandth
0.0000
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Solution to Exercise (p. 4)
Tenth
9.2
Hundredth
9.19
Thousandth
9.192
Table 15
Solution to Exercise (p. 5)
18.417
Solution to Exercise (p. 5)
18.41681
Solution to Exercise (p. 5)
18.42
Solution to Exercise (p. 5)
0.1
Solution to Exercise (p. 5)
0.83607
Solution to Exercise (p. 5)
5.333
Solution to Exercise (p. 5)
Ten million
Solution to Exercise (p. 5)
256
Solution to Exercise (p. 6)
4
3 25
http://cnx.org/content/m34959/1.2/
Ten Thousandth
9.1919