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convert a Recurring Decimal into Vulgar Fraction

May 27, 2020
Category: convert a Recurring Decimal into Vulgar Fraction

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Pure Recurring Decimal into Vulgar Fraction

Write the repeated figure or figures only once in the numerator without decimal point and take as many nines in the denominator as is the number of repeating figures.

e.g. (i) 0.777 . . . = 0. $\overline{7}$ = $\frac{7}{9}$

(ii) 0.035035035 . . . = $0.\overline{035}$ = $\frac{35}{999}$

Mixed Recurring Decimal into Vulgar Fraction

In the numerator take the difference between the number formed by all the digits after decimal point ( taking repeated digits only once ) and that formed by the digits which are not repeated. In the denominator, take the number formed by as many nines as there are repeating digits followed by many zeros as is the number of non-repeating digits.

e.g. (i) 0.5777 . . . = $0.5\overline{7}$ = $\frac{57-5}{90}$ = $\frac{52}{90}$ = $\frac{26}{45}$