Question

Express 0.123 (Bar on 3) in p/q form

Plz give the answer step by step.

Answer 1

Let it be equal to x.

So,

x = 0.12333..... (1)

Multiply (1) by 1000 to get the first three digits after decimal.

==> 1000x = 123.333... (2)

Again, Multiply (1) by 100 to get the first two digits of the decimal expansion.

==> 100x = 12.33333... (3)

Now,

Subtract (3) from (2)

==> 1000x - 100x = 123 - 12

{ .333... cancels out }

==> 900x = 111

==> x = 111/900

Hence, The p/q form of the given decimal expansion is 111/900

Answer 2

____Hope it's helpful_____