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

Question

Question

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

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Mathematics Xavia 4 years 2021-09-05T07:59:34+00:00 2021-09-05T07:59:34+00:00 1 Answers 10 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Jezebel · Answer 1 · 2021-09-05T08:01:28+00:00

Jezebel

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2021-09-05T08:01:28+00:00 September 5, 2021 at 8:01 am

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Given:

Two numbers are $\dfrac{9}{7}$ and $\dfrac{10}{7}$ .

To find:

A repeating decimal that is between $\dfrac{9}{7}$ and $\dfrac{10}{7}$ .

Solution:

Using calculator, we get

$\dfrac{9}{7}=1.285714285714...$

$\dfrac{9}{7}=1.\overline{285714}$

and,

$\dfrac{10}{7}=1.42857142857 1...$

$\dfrac{10}{7}=1.\overline{428571}$

Now, the repeating decimal that is between $\dfrac{9}{7}$ and $\dfrac{10}{7}$ 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 $\dfrac{4}{3}$ .

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