Question

Write the decimal number 2.375375375....... in the form p/q in the simplest form.

Answer 1

Let x = 2.375375375375...
Then 1000x =2375.375375......
1000x - x = 2375.375375... - 2.375375375375.....
999x =  2373
x = $\frac{2373}{999}$

Simplest form = $\frac{791}{333}$