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Module 3: Decimals

Converting from Fractions to Decimals

Tutorial 18: How to Convert (General Case)

Example:

1 5 8 {"version":"1.1","math":"1\dfrac{5}{8}"}

 

  1. If working with a mixed fraction, put the whole off to the side for now and deal with the fraction.

    1 5 8 → o m i t 1 f o r n o w → 5 8 {"version":"1.1","math":"1\frac{5}{8}\rightarrow\;omit\;1\;for\;now\;\rightarrow\;\frac{5}{8}"}

  2. Then divide:

    0.625 8 5.000 − 0 50 − 48 20 − 16 40 − 40 0 {"version":"1.1","math":"\begin{array}{r}0.625\;\\ 8\enclose{longdiv}{5.000}\\{-}0\;\;\;\;\;\;\;\\ \hline 50\;\;\;\;\;\\ {-}48\;\;\;\;\;\\ \hline 20\;\;\;\\ {-}16\;\;\;\\ \hline 40\;\;\\ {-}40\;\;\\ \hline 0\;\; \end{array}"}

  3. Then add 1 to 0.625 → 1.625
  1. Convert the mixed fraction to an improper fraction.

    1 5 8 = 13 8 {"version":"1.1","math":"1\frac{5}{8} = \frac{13}{8}"}

  2. Then divide:

    1.625 8 13.000 − 8 50 − 48 20 − 16 40 {"version":"1.1","math":"\begin{array}{r}1.625\;\\ 8\enclose{longdiv}{13.000}\\{-}8\;\;\;\;\;\;\;\\ \hline 50\;\;\;\;\;\\ {-}48\;\;\;\;\;\\ \hline 20\;\;\;\\ {-}16\;\;\;\\ \hline 40\;\;\;\end{array}"}

Tutorial 19: How to Convert From (Power of 10 Shortcut)

Example:

67 50 {"version":"1.1","math":"\dfrac{67}{50}"}

 

  1. If working with a mixed fraction, put the whole off to the side for now and deal with the fraction.

    67 50 → 1 17 50 → omit 1 for now → 17 50 {"version":"1.1","math":"\dfrac{67}{50} \rightarrow 1\dfrac{17}{50} \rightarrow \mathrm{omit \; 1 \; for \; now} \rightarrow \dfrac{17}{50} "}

  2. Look out for denominators that are factors (or multiples) of any power of 10 (10, 100, 1000, etc.). This fraction can be reduced/multiplied appropriately to obtain these denominators.

    ex. 50 is a multiple of 10. While the fraction can’t be reduced to get a denominator of 10, it can be multiplied to get 100 instead as follows:

    17 50 × 2 2 = 34 100 {"version":"1.1","math":"\dfrac{17}{50} \times \dfrac{2}{2} = \dfrac{34}{100} "}

  3. Once the fraction has been appropriately converted, recall the rules for converting decimal → fraction and work backwards. If there was a whole omitted, add it back as a whole in the decimal.

    34 100 → 0.34 → add 1 whole back → 1.34 {"version":"1.1","math":"\dfrac{34}{100} \rightarrow 0.34 \rightarrow \mathrm{add \; 1 \; whole \; back} \rightarrow 1.34 "}

  1. Look out for denominators that are factors (or multiples) of any power of 10 (10, 100, 1000, etc.). This fraction can be reduced/multiplied appropriately to obtain these denominators.

    67 50 × 2 2 = 134 100 {"version":"1.1","math":"\dfrac{67}{50} \times \dfrac{2}{2} = \dfrac{134}{100} "}

  2. Once the fraction has been appropriately converted, recall the rules for converting decimal → fraction and work backwards.

    134 100 → 1.34 {"version":"1.1","math":"\dfrac{134}{100} \rightarrow 1.34 "}

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