89.7k views
19 votes
What is the difference between a rational and irrational number?

User Skuda
by
7.8k points

1 Answer

6 votes

Answer:

Rational numbers are the numbers which are integers and fractions

Irrational numbers are the numbers whose expression as a fraction is not possible

Examples of Rational Number

1/9 – Both numerator and denominator are integers.

7 – Can be expressed as 7/1, wherein 7 is the quotient of integers 7 and 1.

√16 – As the square root can be simplified to 4, which is the quotient of fraction 4/1

0.5 – Can be written as 5/10 or 1/2 and all terminating decimals are rational.

0.3333333333 – All recurring decimals are rational.

Examples of Irrational Number

√2 – √2 cannot be simplified and so, it is irrational.

√7/5 – The given number is a fraction, but it is not the only criteria to be called as the rational number. Both numerator and denominator need to integers and √7 is not an integer. Hence, the given number is irrational.

3/0 – Fraction with denominator zero, is irrational.

π – As the decimal value of π is never-ending, never-repeating and never shows any pattern. Therefore, the value of pi is not exactly equal to any fraction. The number 22/7 is just and approximation.

0.3131131113 – The decimals are neither terminating nor recurring. So it cannot be expressed as a quotient of a fraction.

User Ian Wong
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories