Question

easy formula of express 0.123333... in p/q form

Answer 1

Here we can see that, after 12, 3 is being repeated, So it is rational, and we can express it in p/q form, here is the solution for it !

Let x = 0.1233333........, Multiply both sides with 1000,

=> 1000x = 123.33333....., Now subtract both the equations,

=> 1000x - x = (123.333...) - (0.123...)
=> 999x = 123.21
=> x = 123.21/999
=> x = 12321/99900,

We at first assigned variable x to 0.123... but at last we got it as 12321/99900,

So, Therefore 0.123.... in p/q form is 12321/99900,

Hope you understand, Have a great day !
Thanking you, Bunti 360 !