Question

Write a real number with ten digits to the right of the decimal point need help with A. And B.

Answer 1

a.
`(12)/(99)=0.121212...`

b.
`√(2)=1.414....`

Explanation:

Given.

A rational number greater than -10 with a 2 digit repeating pattern.

An irrational number between 1 and 2?

(a)

A rational number is one which can be represented in the form
`(p)/(q)` where 'p' and 'q' are integers. A repeating decimal is a rational number as it can be expressed in the form of
`(p)/(q)`.

Therefore, a number which is repeating decimal with 2 of its digits being repeated is
`(12)/(99)=0.121212...`. Here the two digits that are being repeated are 1 and 2.

(b)

An irrational number is one which can't be expressed in the form
`(p)/(q)`. A number which is non-repeating in the interval 1 and 2 is an example of irrational number.

So, a number which is irrational in the interval (1, 2) is
`\sqrt2=1.414....`.