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1.7: Decimal Fractions

  • Page ID
    49343
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    Overview

    • Decimal Fractions
    • Adding and Subtracting Decimal Fractions
    • Multiplying Decimal Fractions
    • Dividing Decimal Fractions
    • Converting Decimal Fractions to Fractions
    • Converting Fractions to Decimal Fractions

    Decimal Fractions

    Fractions are one way we can represent parts of whole numbers. Decimal fractions are another way of representing parts of whole numbers.

    Decimal Fractions

    A decimal fraction is a fraction in which the denominator is a power of 10.

    A decimal fraction uses a decimal point to separate whole parts and fractional parts. Whole parts are written to the left of the decimal point and fractional parts are written to the right of the decimal point. Just as each digit in a whole number has a particular value, so do the digits in decimal positions.

    clipboard_ea88b986766aeb75f89f9bd0ff13a57fa.png

    Sample Set A

    The following numbers are decimal fractions

    Example \(\PageIndex{1}\)

    57.9

    The 9 is in the tenths position. 57.9 = \(10\dfrac{9}{10}\).

    Example \(\PageIndex{2}\)

    6.8014

    The 8 is in the tenths position.

    The 0 is in the hundredths position.

    The 1 is in the thousandths position.

    The 4 is in the ten thousandths position.

    6.8014 = \(6\dfrac{8014}{10000}\).

    Adding and Subtracting Decimal Fractions

    Adding/Subtracting Decimal Fractions:

    To add or subtract decimal fractions,

    1. Align the numbers vertically so that the decimal points line up under each other and corresponding decimal positions are in the same column. Add zeros if necessary.
    2. Add or subtract the numbers as if they were whole numbers.
    3. Place a decimal point in the resulting sum or difference directly under the other decimal points.

    Sample Set B

    Find each sum or difference

    Example \(\PageIndex{3}\)

    clipboard_eb8f3187bed3dae27998d45d92fb02733.png

    Example \(\PageIndex{4}\)

    clipboard_e347c7001e47b6cc97bc4ef4184aad64f.png

    Example \(\PageIndex{5}\)

    clipboard_e78931fdcd0ab185080223fb89a946e6e.png

    Multiplying Decimal Fractions

    Multiplying Decimal Fractions

    To multiply decimals,

    1. Multiply the numbers as if they were whole numbers.
    2. Find the sum of the number of decimal places in the factors.
    3. The number of decimal places in the product is the sum found in step 2.

    Sample Set C

    Find the following products

    Example \(\PageIndex{6}\)

    clipboard_e9a2205a67b0ff9b184b9e94b27f5300c.png

    Example \(\PageIndex{7}\)

    clipboard_e7fe21e750898d21ed9851636a9a8e0c1.png

    Dividing Decimal Fractions

    Dividing Decimal Fractions

    To divide a decimal by a nonzero decimal,

    1. Convert the divisor to a whole number by moving the decimal point to the position immediately to the right of the divisor’s last digit.
    2. Move the decimal point of the dividend to the right the same number of digits it was moved in the divisor.
    3. Set the decimal point in the quotient by placing a decimal point directly above the decimal point in the dividend.
    4. Divide as usual.

    Sample Set D

    Find the following quotients

    Example \(\PageIndex{8}\)

    clipboard_ec5f32196849d2f0f6febf901572c5361.png

    Example \(\PageIndex{9}\)

    clipboard_e99cc7a86f383544f60a07a618f0dc751.png

    Example \(\PageIndex{10}\)

    clipboard_eddecf73ac4c0ceee99b1eed28da9da56.png

    Converting Decimal Fractions to Fractions

    We can convert a decimal fraction to a fraction by reading it and then writing the phrase we have just read. As we read the decimal fraction, we note the place value farthest to the right. We may have to reduce the fraction.

    Sample Set E

    Convert each decimal fraction to a fraction

    Example \(\PageIndex{11}\)

    clipboard_ee771b2283db4f531418ef8c383937923.png

    Example \(\PageIndex{12}\)

    clipboard_ea884cbe3facd91eae60ea788abe93444.png

    Converting Fractions to Decimal Fractions

    Sample Set F

    Convert the following fractions to decimals. If the division is nonterminating, round to 2 decimal places.

    Example \(\PageIndex{13}\)

    clipboard_ef7a4e04a8fa9406d8f6ff9e0bb74ca7d.png

    Example \(\PageIndex{14}\)

    clipboard_e9f18a5e71406773c7600d66bfb1bca1e.png

    Example \(\PageIndex{15}\)

    clipboard_e22125b2b49cab4acb3a0cbebed1e39e1.png

    Example \(\PageIndex{16}\)

    clipboard_ea42278a4fe104364bee6a2d0c91d0e00.png

    Example \(\PageIndex{17}\)

    clipboard_ecb66dcc55e4885d631a5c0d6cdf38144.png

    Exercises

    For the following problems, perform each indicated operation.

    Exercise \(\PageIndex{1}\)

    1.84 + 7.11

    Answer

    8.95

    Exercise \(\PageIndex{2}\)

    15.015 - 6.527

    Exercise \(\PageIndex{3}\)

    4.904 - 2.67

    Answer

    2.234

    Exercise \(\PageIndex{4}\)

    156.33 − 24.095

    Exercise \(\PageIndex{5}\)

    .0012 + 1.53 + 5.1

    Answer

    6.6312

    Exercise \(\PageIndex{6}\)

    44.98 + 22.8 − 12.76

    Exercise \(\PageIndex{7}\)

    5.0004 − 3.00004 + 1.6837

    Answer

    3.68406

    Exercise \(\PageIndex{8}\)

    1.11 + 12.1212 − 13.131313

    Exercise \(\PageIndex{9}\)

    4.26 ⋅ 3.2

    Answer

    13.632

    Exercise \(\PageIndex{10}\)

    2.97 ⋅ 3.15

    Exercise \(\PageIndex{11}\)

    23.05 ⋅ 1.1

    Answer

    25.355

    Exercise \(\PageIndex{12}\)

    5.009 ⋅ 2.106

    Exercise \(\PageIndex{13}\)

    0.1 ⋅ 3.24

    Answer

    0.324

    Exercise \(\PageIndex{14}\)

    100 ⋅ 12.008

    Exercise \(\PageIndex{15}\)

    1000 ⋅ 12.008

    Answer

    12,008

    Exercise \(\PageIndex{16}\)

    10,000 ⋅ 12.008

    Exercise \(\PageIndex{17}\)

    75.642 ÷ 18.01

    Answer

    4.2

    Exercise \(\PageIndex{18}\)

    51.811 ÷ 1.97

    Exercise \(\PageIndex{19}\)

    0.0000448 ÷ 0.014

    Answer

    0.0032

    Exercise \(\PageIndex{20}\)

    0.129516 ÷ 1004

    For the following problems, convert each decimal fraction to a fraction.

    Exercise \(\PageIndex{21}\)

    0.06

    Answer

    \(\dfrac{3}{50}\)

    Exercise \(\PageIndex{22}\)

    0.115

    Exercise \(\PageIndex{23}\)

    3.7

    Answer

    \(3\dfrac{7}{10}\)

    Exercise \(\PageIndex{24}\)

    48.1162

    Exercise \(\PageIndex{25}\)

    712.00004

    Answer

    \(712\dfrac{1}{25000}\)

    For the following problems, convert each fraction to a decimal fraction. If the decimal form is nonterminating,round to 3 decimal places.

    Exercise \(\PageIndex{26}\)

    \(\dfrac{5}{8}\)

    Exercise \(\PageIndex{27}\)

    \(\dfrac{9}{20}\)

    Answer

    0.45

    Exercise \(\PageIndex{28\)

    15 ÷ 22

    Exercise \(\PageIndex{29}\)

    \(\dfrac{7}{11}\)

    Answer

    0.636

    Exercise \(\PageIndex{30}\)

    \(\dfrac{2}{9}\)


    This page titled 1.7: Decimal Fractions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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