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

Question

asked Jan 28, 2021 108k views

1 Answer

Peter Porfy · Answer 1 · 2021-02-02T23:41:55+0000

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
$1.\overline{3}$ .