Number Systems Test - 4

 2, 3

Because it is the square of 14 and can be 

Written in the form of p/q

10/14

Rational numbers can be represented in decimal forms rather than representing in fractions. They can easily be represented as decimals by just dividing numerator ‘p’ by denominator ‘q’ (as rational numbers is in the form of p/q).

A rational number can be expressed as a terminating or nonterminating, recurring decimal.

For example:

(i) 5/2 = 2.5, 

2/8= 0.25, 

7 = 7.0, etc., are rational numbers which are terminating decimals.

(ii) 5/9 = 0.555555555……. = 0.5 ̇,

1/6 = 0.166666 ….. = 0.16 ̇

9/11= 0.818181…… = 0.8 ̇1 ̇ etc., are rational numbers which are nonterminating, recurring decimals.

An irrational number can not be written in the form of p/q

And decimal representation of it is neither terminating nor repeating.

Between any two rational number there are many rational number,

Example — 4 and 8

We have 5,6,7,7.5,,,,,,, and many more

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Difference of two irrationals need not be an irrational.

Example—each one of (5 + √2) and (3 — √2) is irrational.

But, (5+√2) — (3+√2) = 2, which is rational.

π is irrational because 22/7 is not the exact value of π

But,here 22/7 is fraction so ,it is rational