Question

If 12.287287287........ can be represented in $\frac{p}{q}$ form, then 'p - q ' is

• A. 11266
• B. 11176
• C. 11277
• D. 11276

Answer 1

The correct option is D 11276

Let x = 12.287287287..... --- (i)
here the periodicity of the decimal is three.
So we multiply both sides of (i) by 1000, we get

1000x = 12287.287287287--(ii)
Subtract (i) from (ii), we have

1000x = 12287.287287287
- x = 12.287287287
----------------------------------
999x = 12275.000000000.....

x = $\frac{12275}{999}$

p = 12275 and q = 999

So, p-q = 11276.