Question

express 0.26bar as a rational number​

Answer 1

Answer:

x=0.262626

multiply by 100 on both sides

100x=26.2626

equation 1 - equation 2

100x=26.2626

-x=0.2626

______________

99x=26

x=26/99

Step-by-step explanation:

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Answer 2

The rational form of 0. $\overline{26}$ is 26/99.

Given:

A non-terminating number 0. $\overline{26}$.

To Find:

0. $\overline{26}$ as a rational number.

Solution:

We a given a non-terminating number, 0. $\overline{26}$. This number does not terminate or end.

0. $\overline{26}$ = 0.262626.......

This number cannot be written in the p/q form of a fraction and so, is irrational.

A rational number is any number that can be expressed as a fraction (has a non-zero denominator).

Let us convert this number into a rational number using the following steps.

Step 1: Let us assume that x = 0. $\overline{26}$ = 0.2626....           .............................(I)

Step 2: On multiplying both sides by 100, we get:

100x = 26.2626.....                                           .............................(II)

Step 3: Subtract equation (II) from (I).

100x - x = 26.2626 - 0.2626.....

⇒ 99x = 26

⇒ x = 26/99.

∴ The rational form of 0. $\overline{26}$ is 26/99.

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