Decimal to Fraction

Some decimals are just approximations or estimates of a certain number while other fractions represent the exact value of it.

In some situations like measuring ingredients, it is appropriate to use fractions rather than decimals.


Decimal to Fraction Conversion Examples


Example 1:
 3/8

Explanation:

The decimal is terminating.
  •   Change the decimal into a fraction by using the decimal number as the numerator and put 1 as the denominator.
  • `0.375/1`
  •   Move the decimal point of the numerator to the right until it becomes a whole number.
  •   `0.375` `->` `375`. This requires moving decimal point to 3 places to the right to make it a whole number.
  •   Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves which is 3. and hence 1 in denominator become 1000.
  •   The fraction would be `375/1000`.
  •    Reduce to lowest terms :
    `375/1000` = `(3 × 5 × 5 × 5)/(2 × 2 × 2 × 5 × 5 × 5)` = `3/(2 × 2 × 2)` = `3/8`
  • Therefore, `0.375` in fraction is `3/8`.

Example 2:
 3/5

Explanation:

Simplification Steps:

  •   Convert into a fraction format by using the decimal number as the numerator and put 1 as the denominator.
    `0.6/1`
  •   Move the decimal point of the numerator to the right until it becomes a whole number.
    `0.6` `->` `6`.
  •   The decimal point moved 1 decimal places to the right.
    Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves which is 1 and hence 1 in denominator `->` 10.
  •   The fraction would be `6/10`. Reduce to lowest terms: `6/10` = `(3 × 3)/(2 × 5)` = `3/(5)` = `3/5`

Therefore, `0.6` in fraction is `3/5`.


Example 3:

 4/33

Explanation:

The decimal is non-terminating.
Multiply the decimal by a power of 10 that will move the repeating digit/s to the left of the decimal point. Use 100 since there are 2 digits repeating.
`0.1212 × 100 = 12.12 `
Divide the repeating digits by the difference between the power of 10 used to multiply the decimal and 1.
`12/(100-1)` = `12/99`
Reducing to lowest terms;
`12/99` = `(2 × 2 × 3)/(3 × 3 × 11)` = `(2 × 2)/(3 × 11)` = `4/33`
Therefore, the fraction form of `0.1212 ` is `4/33`.


Example 4:
 5/8

Explanation:

The decimal is terminating.

  •   Move the decimal point of the numerator to the right until it becomes a whole number.
    `0.625` `->` `625`.
  •   The decimal point moved 3 decimal places to the right.
    Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves (i.e 3 places). Thus 1 in denominator `->` 1000.
  •   The fraction would be `625/1000`. Reduce to lowest terms. `625/1000` = `(25 × 25)/(2 × 5 × 100)` = `(5 × 5 × 5 × 5)/(2 × 5 × 2 × 5 × 2 × 5 ×)` = `5/8`

Therefore, `0.625` in fraction is `5/8`.


Example 5:
 1/8

Explanation:

The decimal number doesn't contain repated number and hence it is terminating.

  •   Move the decimal point of the numerator to the right until it becomes a whole number.
    `0.125` `->` `125`.
  •   The decimal point moved 3 decimal places to the right.
    Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves(i.e. 3). This makes denomiantor 1 to become `->` 1000.
  •   The fraction would be `125/1000`.
  • Reduce to lowest terms:
    `125/1000` = `(25 × 5)/(2 × 5 × 100)` = `(5 × 5 × 5)/(2 × 5 × 2 × 5 × 2 × 5)` = `1/8`

Therefore, `0.125` in fraction is `1/8`.


 Steps for converting Decimals to Fractions

If Decimal is terminating

  •  Change the decimal into fraction form by using the decimal number as the numerator and put 1 as the denominator.
  •  Move the decimal point of the numerator to the right until it becomes a whole number.
  •  Move the decimal point of the denominator to the right by the same number of places that the decimal point of the numerator moves. Place a zero (0) if the decimal point have move to a decimal place without a digit.
  •  Reduce the fraction into lowest terms.

If Decimal is non-terminating (continuous)

  •  Multiply the decimal by a power of 10 that will move the digit/s which is/are repeating to the left of the decimal point. The number of zeros (0) of the power of 10 to be multiplied depends on the number of digits that repeats.
  •  Divide the repeating digits by the difference between the power of 10 used to multiply the decimal and 1.
  •  Reduce to lowest terms.





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