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2.1: Understanding Decimals

  • Page ID
    7086
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    Numbers written with decimals is another way of expressing fractions. However, decimals have a distinct differentiation with fractions in that decimals are based on 10. In that, one decimal place to the right of the whole number indicates tenths, two decimal places to the right of the whole number indicates hundredths, three decimal places to the right of the whole number indicates thousandths, etc.

    Example \(\PageIndex{1}\)

    0.1 = tenths place

    1.01 = hundredths place

    0.001 = thousandths place

    1.01 = ten thousandths place

    Decimals can easily be written as fractions by using the number to the right of the decimal point as the numerator and then using a 10, 100, 1,000, 10,000, etc. as the denominator. Determining which “base-ten” number to use as the denominator is determined by the number of digits there are to the right of the decimal point.

    Example \(\PageIndex{2}\)

    \(\begin{array}{ll}
    0.1 \rightarrow \dfrac{1}{10} & 1 \text { tenth } \\
    0.01 \rightarrow \dfrac{1}{100} & 1 \text { hundredth } \\
    0.001 \rightarrow \dfrac{1}{1,000} & 1 \text { thousandth } \\
    0.0001 \rightarrow \dfrac{1}{10,000} & 1 \text { ten-thousandth }
    \end{array}\)

    Exercise 2.1

    Write the following decimals as fractions and reduce if necessary.

    1. 0.2 =
    2. 0.103 =
    3. 0.13 =
    4. 0.02 =
    5. 0.1234 =
    6. 0.0023 =
    7. 0.0101 =
    8. 0.1010 =
    9. 0.020 =
    10. 0.0202 =
    11. 0.1000 =
    12. 0.4500 =

    Exercise 2.1.1

    Write the following expressions as decimals and fractions.

    Decimal

    Fraction

    7 tenths

    1,000 ten-thousandths

    475 thousandths

    32 hundredths

    12 thousandths

    2,345 ten-thousandths

    3 hundredths

    10 thousandths

    132 ten-thousandths

    4,002 ten-thousandths

    Digits to the left of the decimal indicate a whole number. Whenever there is a whole number with a decimal fraction the expression is pronounced using “and.”

    Example:

    12.3 = Twelve and three tenths = \(12 \dfrac{3}{10}\)

    100.07 = One hundred and seven hundredths = \(100 \dfrac{7}{100}\)

    3,005.023 = Three thousand five and twenty-three thousandths = \(3,005 \dfrac{23}{1,000}\)

    Exercise 2.1.2

    Write the following expressions as a decimal and a fraction. Remember to reduce if necessary.

    Decimal

    Fraction

    Two and five hundredths

    Thirteen and two hundred thousandths

    One thousand three and two ten-thousandths

    Fifty-five and fifty hundredths

    One and fourteen hundredth

    Eleven thousand four and twelve thousandths

    Ten and two tenths

    Four hundred one and four ten-thousandths

    Five thousand two hundred eight and one thousand ten-thousandths


    2.1: Understanding Decimals is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.

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