Question

Part B: Find an irrational number that is between 9.5 and 9.7. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.

Answer 1

Answer:

Step-by-step explanation:

Also, to explain the reason behind being irrational and include the decimal approximation of the irrational number to the nearest hundredth.

We know that

a number is irrational if the digits after the decimal are non-terminating and non-repeating.

Let x be an irrational number between 9.5 and 9.7.

So, we consider that

x = 9.562536941412578914.........

We can see that the digits after the decimal are non-terminating and non-repeating. so, the number is irrational.

Rounding to the nearest hundredth, we get

x = 9.56.

Thus, the required number is 9.56.