Given Question -

Express the following decimal in the form p/q, where p, q are integers and q ≠ 0 , 0.1 38bar.

Required Answer -

In the portion it is not defined properly that bar is on which number . But bar can be on

• 8
• 38
• 138

So let's do the all three cases

I Case -

If the bar is on 8

Let 0.1388888... be x

Multiplying both side with 100,

....(i)

Multiplying both side with 10

....(ii)

Now subtract (i) from (ii)

As we know that .888... Is non terminating so there will be no change if we write it as zero on subtracting .

If you will convert it again into decimal then you will get result as 0.13(8)bar only

__________________

II Case -

If the bar is on 38

Let 0.138383838... be x

Multiplying both side with 10,

....(i)

Multiplying both side with 100

....(ii)

Now subtract (i) from (ii)

As we know that .383838... Is non terminating so there will be no change if we write it as zero on subtracting .

If you will convert it again into decimal then you will get result as 0.1(38)bar only

__________________

III Case -

If the bar is on 138

Let 0.138138138138138... be x

....(i)

Multiplying both side with 1000,

....(ii)

Now subtract (i) from (ii)

As we know that .138138138... Is non terminating so there will be no change if we write it as zero on subtracting .

If you will convert it again into decimal then you will get result as 0.(138)bar only

Given Question -

Express the following decimal in the form p/q, where p, q are integers and q ≠ 0 , 0.1 38bar.

Required Answer -