Question

0.5 Express 1.27272727.... in the form p/q
15/11
16/11
оооо
14/11
12/11​

Answer 1

Given:

• A number Irrational number is given to us i.e. 1.27272727......

To Find:

• To express it in the form of p/q where p and q are integers and q≠0.

Answer:

It's given that there is a Irrational number i.e. 1.272727.....

Let us take that x =1.27272727...

Now 100x =100×1.2727...= 127.27272727....

And 10000x = 10000×1.272727....=

12727.272727....

Let

• 100x = equation (1).
• 10000x = equation (2).

On subtraction of equation 1 from equation 2.,

$\sf{\implies 10000x-100x = 12727.2727...-127.272727...}$

$\sf{\implies 9900x = 12600}$

$\sf{\implies x=\dfrac{12600}{9900}}$

${\underline{\boxed{\red{\sf{\leadsto x=\dfrac{14}{11}}}}}}$

Hence our reqiured answer is $\sf{\bold{\dfrac{14}{11}}}$ .