Integers Integers are further classified into natural number, whole number. So, first we talk about the first form of integer which means natural number. Natural number : - Natural number is a number which is called simple counting. Simple counting means the counting which we teach a L.K.G. s tudents. For example 1, 2, 3, 4, 5, 6, 7, 8, 9 and so on. Natural number can be represented by (N). Then we talk about second form of integers which mean whole number. Whole number : - W hole number include natural number and zero. Whole number can be represented by (W).for example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and so on. So, we understand that what is whole and natural numbers. Then we talk about integers. Integers : - Integers are include natural number, whole number and negative numbers. Integers can be represented by (Z). For example -1, -2, -3, -4, -5 and so on.

Practice Questions :

Practice Questions We have understand about integer and its type. So, I have question for you. What are the types of integers? Natural number and decimal (b) whole and rational numbers (c ) natural number and whole number 2. Natural number can be also called __________ (a) Integers (b) simple counting (c) decimal form (d) natural numbers 3. 1, 2, 3, 4, 5, 6, 7, 8, 9 and so on is a Natural number (b) F ractional form (c) decimal form (d) negative form 4. Natural number is represented by __________ (a) N (b) M (c) Q (d) Z

Practice question (continued):

Practice question (continued) 5. Whole number include natural number and __________ Negative number (b ) zero ( c ) fraction form ( d) decimal form 6. Whole number can be represented by __________ (a ) Z ( b ) M ( c ) N ( d) W 7. -1 is a whole number. ( a) True ( b ) False 8. Integers include natural number, whole number and __________ ( a) Negative number (b ) fraction form (c ) zero (d) rational number 9. Integers can be represented by __________ . (a ) I ( b ) Z ( c ) F (d) L

Answers:

Answers Answers of practice questions Question number 1 Answer : - natural and whole number Question number 2 Answer: - simple counting Question number 3 Answer : - natural number Question number 4 Answer : - N

Answers of practice questions (continued):

Answers of practice questions (continued) Answers of practice questions Question number 5 Question number 9 Answer : - zero Answer : - Z Question number 6 Answer : - W Question number 7 Answer : - false Question number 8 Answer : - negative number

Rational number:

Rational number Now, we understand and we practice that what is integer and its type. So, now we understand about rational number and its types Fraction form Decimal form I ntegers Rational numbers types

Decimal form of rational number:

Decimal form of rational number We know the first form of rational numbers is integer but we know about integers so, we understand about second type of rational numbers which mean decimal form. The decimal form means in rational numbers that the decimal number have to be recurring and terminating. For example : - 0.33113311, 0.1111111111111 etc It is not always that rational number have to be recurring and terminating. It can be also only terminating. For example :- 0.10, 0.195, 0.123456 e.t.c. It can be also only have recurring. For example :- 0.123123…….. e.t.c, 0.191919….. e.t.c, 0.25252….. e.t.c.

Fractional form:

Fractional form Fractional form is the basic form of rational number. This form we have learnt in smaller classes. Let’s revised it. fractional numbers are in the p/q form where q ≠ 0. For example ¼, ½, ¾ . We know we can make decimal form into fractional form. For example :- 0.10 = 1/10 etc. We can also represent fractional form in the number line. It is also possible that we can represent decimal form in the number line.

Irrational numbers:

Irrational numbers Irrational numbers have only one form known as decimal form. Decimal have two rules to become irrational numbers they are non recurring and non terminating. To become irrational numbers it is not necessary that the number have to be non recurring and non terminating. It can be only non recurring but terminating. For example :- 0.12323145, 0.23568941, 0.36974125, 0.58931764, 0.537914628, 0.123045607890,0.1233456678990. It can be only non terminating but recurring. For example :- 0.123123…etc, 0.656565…etc, 0.0101…etc, 0.363636….etc, 0.145145….etc, 0.22222…etc. So, we have learnt irrational number and rational number and so on. Let’s learn about real number in next slide.

Real numbers:

Real numbers All the form the numbers are called real number Basically real number catorcorised into two forms they are rational numbers and irrational numbers. That we have learnt into earlier slides. It considered that natural, whole, integers, rational and irrational numbers are the real numbers.

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