Class 9 Math Exercise 1.3 | Question 4

Question 4: Express 0.\\overline{9}) in the form \\frac{p}{q})

Explanatory Answer | Exercise 1.3 Question 4

Let 0.\\overline{9}) be x.
As there is only one digit that is recurring, we must multiply by 10.
So, 10x = 9.99999999...
x = 0.999999999
Therefore, 10x = 9 + x
Or 9x = 9
x = 1
So, 0.\\overline{9}) = 1