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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 [link] 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. less than 5 . If so, leave the round-off digit unchanged.
    2. 5 or greater . If so, add 1 to the round-off digit.
  3. If the round-off digit is
    1. to the right of the decimal point, eliminate all the digits to its right.
    2. 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.)

Round 32.116 to the nearest hundredth.

  • 1 is in the hundredths position of 32.116

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

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

  • 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.

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Round 633.14216 to the nearest hundred.

  • 6 is in the hundreds position of 633.14216

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

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1,729.63 rounded to the nearest ten is 1,730.

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1.0144 rounded to the nearest tenth is 1.0.

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60.98 rounded to the nearest one is 61.

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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).

67.129 rounded to the second decimal place is 67.13.

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67.129558 rounded to 3 decimal places is 67.130.

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Practice set a

Round each decimal to the specified position.

4.816 to the nearest hundredth.

4.82

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0.35928 to the nearest ten thousandths.

0.3593

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82.1 to the nearest one.

82

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753.98 to the nearest hundred.

800

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Round 43.99446 to three decimal places.

43.994

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Round 105.019997 to four decimal places.

105.0200

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Round 99.9999 to two decimal places.

100.00

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Exercises

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

20.01071

Tenth Hundredth Thousandth Ten Thousandth
Tenth Hundredth Thousandth Ten Thousandth
20.0 20.01 20.011 20.0107
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3.52612

Tenth Hundredth Thousandth Ten Thousandth
3.53
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531.21878

Tenth Hundredth Thousandth Ten Thousandth
Tenth Hundredth Thousandth Ten Thousandth
531.2 531.22 531.219 531.2188
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36.109053

Tenth Hundredth Thousandth Ten Thousandth
36.1
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1.999994

Tenth Hundredth Thousandth Ten Thousandth
Tenth Hundredth Thousandth Ten Thousandth
2.0 2.00 2.000 2.0000
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7.4141998

Tenth Hundredth Thousandth Ten Thousandth
7.414
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0.000007

Tenth Hundredth Thousandth Ten Thousandth

Tenth Hundredth Thousandth Ten Thousandth
0.0 0.00 0.000 0.0000

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0.00008

Tenth Hundredth Thousandth Ten Thousandth
0.0001
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9.19191919

Tenth Hundredth Thousandth Ten Thousandth

Tenth Hundredth Thousandth Ten Thousandth
9.2 9.19 9.192 9.1919

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0.0876543

Tenth Hundredth Thousandth Ten Thousandth
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Calculator problems

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

3 decimal places.

18.417

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5 decimal places.

18.41681

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Calculator problems

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

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

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

0.1

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

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

0.83607

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

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

5.333

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

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Exercises for review

( [link] ) What is the value of 2 in the number 421,916,017?

Ten million

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( [link] ) Perform the division: 378 ÷ 29 size 12{"378 " div " 29"} {} .

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( [link] ) Find the value of 4 4 size 12{4 rSup { size 8{4} } } {} .

256

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( [link] ) Convert 11 3 size 12{ { {"11"} over {3} } } {} to a mixed number.

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( [link] ) Convert 3.16 to a mixed number fraction.

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

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Questions & Answers

explain and give four Example hyperbolic function
Lukman Reply
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
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Harshika Reply
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Harshika
find the subring of gaussian integers?
Rofiqul
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Shirley Reply
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Mark
I need quadratic equation link to Alpa Beta
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find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
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use the y -intercept and slope to sketch the graph of the equation y=6x
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4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
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how do you translate this in Algebraic Expressions
linda Reply
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Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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