Number System | Interesting number facts | Introduction to Rational Numbers

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• Natural Numbers: The numbers 1, 2, 3, which are believed to be first used by human beings in a natural way for counting the objects are called natural numbers. The collection of natural numbers is denoted by ‘N’.

• Whole Numbers: The natural numbers along with the number O i.e. 0, 1, 2, 3,4... are called Whole numbers. The collection of these numbers is denoted by ‘WI.

• Integers: Whole numbers along with the numbers like... -4, -3, -2, -1, form a collection of numbers called integers. This collection is denoted by ‘Z’ or ‘I’. Letter Z has been taken from a German word ‘Zohlen’ which means ‘to count’. 1, 2, 3 are positive integers. .. .-4, -3, -2, -1 are negative integers and 0 is neither positive nor negative.

• Rational Number: A number which can be expressed in the form p/q, where p and q are integers, q is not zero.

• Equivalent Rational Numbers: If p/q is a rational number, then, we can obtain its equivalent rational number by multiplying its numerator and denominator by the same non-zero number.

Number Facts

1. All natural numbers are rational numbers.

2. All fractionas are rational numbers.

3. All Whole numbers are rational numbers.

4. All integers are rational numbers.

00:02 Q1. State whether the following statements are true or false. Justify your answers.

00:17 (i) Every irrational number is a real number.

00:25 Tree diagram of Types of numbers.

00:40 (ii) Every point on the number line is of the form sqrt(m) , where m is a natural number.

01:06 (iii) Every real number is an irrational number.

01:31 Explanation of Every real number is not an irrational number

01:54 Q4. State whether the following statements are true or false. Give reasons for your answers.

02:10 (i) Every natural number is a whole number.

02:24 Explanation of number fact that Every natural number is a whole number

02:31 (ii) Every integer is a whole number.

02:56 (iii) Every rational number is a whole number.

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