Question

Is 0.920920092000...a rational or an irrational​

Answer 1

rational number

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Answer 2

Answer : -

It's an irrational number.

Explaination : -

As we know that, a rational number is terminating or repeating. There, a single number, or a block of numbers should be repeating so that it can be called as a rational number.

For example = 0.9999999.....

Here, one number is repeating, so it can be called as a rational number.

Rational number can be defined as,

A number which can be written in the form of $\frac{p}{q}$ where q ≠ 0.

We can also write the number 0.999999..... in the form of $\frac{p}{q}$ where q is not equal to 0 as demonstrated below alsl p and q are integers.

=> Let x be 0.99999...

Now, 10x = 9.999999......

10x = 9 + x (°.° 0.99999.... is x)

10x - x = 9

9x = 9

x = $\frac{9}{9}$

x = $\frac{1}{1}$

But, x = 0.99999.....

Therefore, 0.9999999..... = $\frac{1} {1}$

Where, p and q both are integers and q is not equal to 0.

But the number 0.920920092000... is neither terminating nor repeating.

Therefore, 0.920920092000... is a irrational number.