Question

express 1.underbar4 as a fraction in simplest form​

Answer 1

HERE'S YOUR ANSWER ⤵⤵⤵⤵⤵

↪X=1.4444444...(1)

↪10X=14.444444...(2)

SO, subtracting EQ 2 from 1 we get,

⚫9X=13

↪X=13/9

Answer 2

Given : We have to convert 1.$\bar{4}$ in fraction form or p/q form. For that, we have to remove bar from the given decimal number, as the number of times of 4 will be infinite, we can subtract it by itself.

Let a = 1.$\bar{4}$ ... ( i )

Multiply both sides by 10 : ( Depend on the numbers under bar. Since there is only one number under bar, multiply by 10 )

= > 10 x a = 10 x ( 1.$\bar{4}$)

= > 10a = 14.$\bar{4}$ { there are infinitely many 4s under bar }

Now, subtract ( i ) from the above equation : ( As we want to remove bar )

10a = 14.$\bar{4}$

- a = - 1. $\bar{4}$

9a = 13 { bar cancelled }

= > a = 13 / 9

= > a = 1.$\bar{4}$ [ As assumed in the starting ] = 13 / 9

Hence the required numeric value of 1.$\bar4$ in fraction form is 13 / 9.

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