Number System | Interesting number facts | Introduction to Rational Numbers
• 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.
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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