Question

find the decimal expansion of 5/7​

Answer 1

Answer:

0.714285714....... is the decimal expansion of 5/7 and it is a non terminating, and repeating decimal expansion.

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Answer 2

The decimal expansion of 5/7 is 0.714285714.

Given,

The rational number = 5/7.

To Find,

The decimal expansion.

Solution,

Before solving the question, let's understand the concept of non-terminating and repeating numbers.

Non-terminating and Repeating Decimals

There are infinite digits in non-terminating decimals, as the decimal expansion never ends. There are decimals after the decimal point that repeat a certain number of digits uniformly.

An example of non-terminating and repeating decimals is 1.868686…Here, the digit 86 constantly repeats after the decimal point.

Note: Non-terminating and repeating decimals are rational numbers.

Now, let's solve the question,

in the given number numerator is 5, and the denominator is 7

So, we have to divide the numerator by the denominator.

= 5 ÷ 7

On dividing, we get,

= 0.714285714

So, the number is non-terminating and repeating because 714 is repeating in the number.

The decimal expansion of 5/7 is 0.714285714.

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