Answer:
a. [tex]\frac{12}{99}=0.121212...[/tex]
b. [tex]\sqrt{2}=1.414....[/tex]
Step-by-step 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 [tex]\frac{p}{q}[/tex] where 'p' and 'q' are integers. A repeating decimal is a rational number as it can be expressed in the form of [tex]\frac{p}{q}[/tex].
Therefore, a number which is repeating decimal with 2 of its digits being repeated is [tex]\frac{12}{99}=0.121212...[/tex]. 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 [tex]\frac{p}{q}[/tex]. 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 [tex]\sqrt2=1.414....[/tex].
