Question

Write a repeating decimal that is between 9/7
and 10/7.
Justify your answer.

Answer 1

Given:

Two numbers are
`(9)/(7)` and
`(10)/(7)`.

To find:

A repeating decimal that is between
`(9)/(7)` and
`(10)/(7)`.

Solution:

Using calculator, we get

`(9)/(7)=1.285714285714...`

`(9)/(7)=1.\overline{285714}`

and,

`(10)/(7)=1.42857142857 1...`

`(10)/(7)=1.\overline{428571}`

Now, the repeating decimal that is between
`(9)/(7)` and
`(10)/(7)` be x. So,

`1.\overline{285714}<x<1.\overline{428571}`

On analyzing the numbers to hundredth places, we get 1.28 < 1.33 < 1.42, therefore

`1.\overline{285714}<1.3333...<1.\overline{428571}`

`1.\overline{285714}<1.\overline{3}<1.\overline{428571}`

And we know that
`1.\overline{3}` is the decimal form of
`(4)/(3)`.

Therefore, the required number is
`1.\overline{3}` .