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Rounding Decimals

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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 specified position.

Section Overview

  • Rounding Decimal Numbers

Rounding Decimal Numbers

We first considered the concept of rounding numbers in (Reference) 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-off digit (with an arrow or check).
  2. Note whether the digit to the immediate right of the marked digit is
    1. (a) less than 5. If so, leave the round-off digit unchanged.
    2. (b) 5 or greater. If so, add 1 to the round-off digit.
  3. If the round-off digit is
    1. (a) to the right of the decimal point, eliminate all the digits to its right.
    2. (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.

Sample Set A

Round each decimal to the specified position. (The numbers in parentheses indicate which step is being used.)

Example 1

Round 32.116 to the nearest hundredth.

  • (1)

    1 is in the hundredths position of 32.116

  • (2b) The digit immediately to the right is 6, and 6 > 56 > 5 size 12{"6 ">" 5"} {}, so we add 1 to the round-off digit:

    1 + 1 = 2 1 + 1 = 2 size 12{"1 "+" 1 "=" 2"} {}

  • (3a) The round-off 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)

    6 is in the hundreds position of 633.14216

  • (2a) The digit immediately to the right is 3, and 3 < 53 < 5 size 12{"3 "<" 5"} {} so we leave the round-off digit unchanged.
  • (3b) The round-off 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-off 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.

Practice Set A

Round each decimal to the specified position.

Exercise 1

4.816 to the nearest hundredth.

Solution

4.82

Exercise 2

0.35928 to the nearest ten thousandths.

Solution

0.3593

Exercise 3

82.1 to the nearest one.

Solution

82

Exercise 4

753.98 to the nearest hundred.

Solution

800

Exercise 5

Round 43.99446 to three decimal places.

Solution

43.994

Exercise 6

Round 105.019997 to four decimal places.

Solution

105.0200

Exercise 7

Round 99.9999 to two decimal places.

Solution

100.00

Exercises

For the first 10 problems, complete the chart by rounding each decimal to the indicated positions.

Exercise 8

20.01071

Table 1
Tenth Hundredth Thousandth Ten Thousandth
       

Solution

Table 2
Tenth Hundredth Thousandth Ten Thousandth
20.0 20.01 20.011 20.0107

Exercise 9

3.52612

Table 3
Tenth Hundredth Thousandth Ten Thousandth
  3.53    

Exercise 10

531.21878

Table 4
Tenth Hundredth Thousandth Ten Thousandth
       

Solution

Table 5
Tenth Hundredth Thousandth Ten Thousandth
531.2 531.22 531.219 531.2188

Exercise 11

36.109053

Table 6
Tenth Hundredth Thousandth Ten Thousandth
36.1      

Exercise 12

1.999994

Table 7
Tenth Hundredth Thousandth Ten Thousandth
       

Solution

Table 8
Tenth Hundredth Thousandth Ten Thousandth
2.0 2.00 2.000 2.0000

Exercise 13

7.4141998

Table 9
Tenth Hundredth Thousandth Ten Thousandth
    7.414  

Exercise 14

0.000007

Table 10
Tenth Hundredth Thousandth Ten Thousandth
       

Solution

Table 11
Tenth Hundredth Thousandth Ten Thousandth
0.0 0.00 0.000 0.0000

Exercise 15

0.00008

Table 12
Tenth Hundredth Thousandth Ten Thousandth
      0.0001

Exercise 16

9.19191919

Table 13
Tenth Hundredth Thousandth Ten Thousandth
       

Solution

Table 14
Tenth Hundredth Thousandth Ten Thousandth
9.2 9.19 9.192 9.1919

Exercise 17

0.0876543

Table 15
Tenth Hundredth Thousandth Ten Thousandth
       

Calculator Problems

For the following 5 problems, round 18.4168095 to the indi­cated place.

Exercise 18

3 decimal places.

Solution

18.417

Exercise 19

1 decimal place.

Exercise 20

5 decimal places.

Solution

18.41681

Exercise 21

6 decimal places.

Exercise 22

2 decimal places.

Solution

18.42

Calculator Problems

For the following problems, perform each division using a calculator.

Exercise 23

4 ÷ 34 ÷ 3 size 12{"4 " div " 3"} {} and round to 2 decimal places.

Exercise 24

1 ÷ 81 ÷ 8 size 12{"1 " div " 8"} {} and round to 1 decimal place.

Solution

0.1

Exercise 25

1 ÷ 271 ÷ 27 size 12{"1 " div " 27"} {} and round to 6 decimal places.

Exercise 26

51÷ 6151÷ 61 size 12{"51" div " 61"} {} and round to 5 decimal places.

Solution

0.83607

Exercise 27

3 ÷ 163 ÷ 16 size 12{"3 " div " 16"} {} and round to 3 decimal places.

Exercise 28

16 ÷ 316 ÷ 3 size 12{"16 " div " 3"} {} and round to 3 decimal places.

Solution

5.333

Exercise 29

26 ÷ 726 ÷ 7 size 12{"26 " div " 7"} {} and round to 5 decimal places.

Exercises for Review

Exercise 30

((Reference)) What is the value of 2 in the number 421,916,017?

Solution

Ten million

Exercise 31

((Reference)) Perform the division: 378 ÷ 29378 ÷ 29 size 12{"378 " div " 29"} {}.

Exercise 32

((Reference)) Find the value of 4444 size 12{4 rSup { size 8{4} } } {}.

Solution

256

Exercise 33

((Reference)) Convert 113113 size 12{ { {"11"} over {3} } } {} to a mixed number.

Exercise 34

((Reference)) Convert 3.16 to a mixed number fraction.

Solution

34253425 size 12{3 { {4} over {"25"} } } {}

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