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6.3: Rounding Decimals

  • Page ID
    48866
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    Learning Objectives
    • be able to round a decimal number to a specified position

    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.

    Solution

    1: 1 is in the hundredths position of 32.116

    2b: The digit immediately to the right is 6, and \(6 > 5\), so we add 1 to the round-off digit:
    \(1 + 1 = 2\)

    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.

    Sample Set A

    Round 633.14216 to the nearest hundred.

    Solution

    1: 6 is in the hundreds position of 633.14216

    2a: The digit immediately to the right is 3, and \(3 < 5\) 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.

    Sample Set A

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

    Sample Set A

    1.0144 rounded to the nearest tenth is 1.0.

    Sample Set A

    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).

    Sample Set A

    67.129 rounded to the second decimal place is 67.13.

    Sample Set A

    67.129558 rounded to 3 decimal places is 67.130.

    Practice Set A

    Round each decimal to the specified position.

    4.816 to the nearest hundredth.

    Answer

    4.82

    Practice Set A

    0.35928 to the nearest ten thousandths.

    Answer

    0.3593

    Practice Set A

    82.1 to the nearest one.

    Answer

    82

    Practice Set A

    753.98 to the nearest hundred.

    Answer

    800

    Practice Set A

    Round 43.99446 to three decimal places.

    Answer

    43.994

    Practice Set A

    Round 105.019997 to four decimal places.

    Answer

    105.0200

    Practice Set A

    Round 99.9999 to two decimal places.

    Answer

    100.00

    Exercises

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

    Exercise \(\PageIndex{1}\)

    20.01071

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

    Exercise \(\PageIndex{2}\)

    3.52612

    Tenth Hundredth Thousandth Ten Thousandth
      3.53    

    Exercise \(\PageIndex{3}\)

    531.21878

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

    Exercise \(\PageIndex{4}\)

    36.109053

    Tenth Hundredth Thousandth Ten Thousandth
    36.1      

    Exercise \(\PageIndex{5}\)

    1.999994

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

    Exercise \(\PageIndex{6}\)

    7.4141998

    Tenth Hundredth Thousandth Ten Thousandth
        7.414  

    Exercise \(\PageIndex{7}\)

    0.000007

    Tenth Hundredth Thousandth Ten Thousandth
           
    Answer
    Tenth Hundredth Thousandth Ten Thousandth
    0.0 0.00 0.000 0.0000

    Exercise \(\PageIndex{8}\)

    0.00008

    Tenth Hundredth Thousandth Ten Thousandth
          0.0001

    Exercise \(\PageIndex{9}\)

    9.19191919

    Tenth Hundredth Thousandth Ten Thousandth
           
    Answer
    Tenth Hundredth Thousandth Ten Thousandth
    9.2 9.19 9.192 9.1919

    Exercise \(\PageIndex{10}\)

    0.0876543

    Tenth Hundredth Thousandth Ten Thousandth
           

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

    Exercise \(\PageIndex{11}\)

    3 decimal places.

    Answer

    18.417

    Exercise \(\PageIndex{12}\)

    1 decimal place.

    Exercise \(\PageIndex{13}\)

    5 decimal places.

    Answer

    18.41681

    Exercise \(\PageIndex{14}\)

    6 decimal places.

    Exercise \(\PageIndex{15}\)

    2 decimal places.

    Answer

    18.42

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

    Exercise \(\PageIndex{16}\)

    \(4 \div 3\) and round to 2 decimal places.

    Exercise \(\PageIndex{17}\)

    \(1 \div 8\) and round to 1 decimal place.

    Answer

    0.1

    Exercise \(\PageIndex{18}\)

    \(1 \div 27\) and round to 6 decimal places.

    Exercise \(\PageIndex{19}\)

    \(51 \div 61\) and round to 5 decimal places.

    Answer

    0.83607

    Exercise \(\PageIndex{20}\)

    \(3 \div 16\) and round to 3 decimal places.

    Exercise \(\PageIndex{21}\)

    \(16 \div 3\) and round to 3 decimal places.

    Answer

    5.333

    Exercise \(\PageIndex{22}\)

    \(26 \div 7\) and round to 5 decimal places.

    Exercises for Review

    Exercise \(\PageIndex{23}\)

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

    Answer

    Ten million

    Exercise \(\PageIndex{24}\)

    Perform the division: \(378 \div 29\).

    Exercise \(\PageIndex{25}\)

    Find the value of \(4^4\).

    Answer

    256

    Exercise \(\PageIndex{26}\)

    Convert \(\dfrac{11}{3}\) to a mixed number.

    Exercise \(\PageIndex{27}\)

    Convert 3.16 to a mixed number fraction.

    Answer

    \(3 \dfrac{4}{25}\)


    This page titled 6.3: Rounding Decimals is shared under a CC BY license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) via source content that was edited to the style and standards of the LibreTexts platform.