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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
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nano basically means 10^(-9). nanometer is a unit to measure length.
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characteristics of micro business
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for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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Do you know which machine is used to that process?
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how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
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What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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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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