Question

Convert 4.13(recurring) into vulgar fraction

Answer 1

Follow the steps for theconversion of mixed recurring decimals into vulgar fractions:

(i) First write the decimal form by removing the bar from the top and put it equal to (any variable). x

(ii) Now, find the number of digits having no bar after the decimal point.

(iii) Suppose there are n-digits without bar, multiply both sides by ${10}^n$, so that only the repeating decimal digit is on the right side of the decimal point.

(iv) Now write the repeating digits at least twice.

(v) Now, find the number of digits having bar after the decimal point.

(vi) Suppose there are n-digits having bar, multiply both sides by ${10}^n$.
(vii) Then subtract the number obtained in step from the number obtained in step (i) and (ii).

(viii) Then divide both the sides of the equation by the coefficient of x.

(ix) Therefore, we get the required vulgar fraction in the lowest form.