Question

Show 0.128...... (bar on 128) in the form of p/q

Answer 1

let 0.128bar=x
multiplying both side by 1000
128.128bar=1000x
128+0.128bar=1000x
128+x=1000x
999x=128
x=128/999=p/q
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Answer 2

Let 'x' be 0.128(bar on 128)

As the number of repeating decimals is 3 we should multiply x ands its value with 1000.

We will get:

1000x=128.128(bar on 128)

Now we should SUBTRACT x from 1000x and even SUBTRACT their values.

We will get:

1000x-x=128.128(bar on 128)-0.128(bar on 128).

999x=128
x=128/999

Therefore,0.128 (bar on 128) in the form of p/q where p and q are integers and q is not equal to 0 is 128/999.