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PPT: Rational Numbers
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Page 1 RATIONAL NUMBERS Page 2 RATIONAL NUMBERS A number of the form P/Q or a number which can be expressed in the form P/Q ,where Pand Q are integers and Q not = 0 , is called a RATIONAL NUMBERS. EXAMPLE – Each of the numbers 2/3 , -5/7 ,-11/-5,7/-9 is a RATIONAL number. But 2/0,-5/0 are not RATIONALnumbers. Page 3 RATIONAL NUMBERS A number of the form P/Q or a number which can be expressed in the form P/Q ,where Pand Q are integers and Q not = 0 , is called a RATIONAL NUMBERS. EXAMPLE – Each of the numbers 2/3 , -5/7 ,-11/-5,7/-9 is a RATIONAL number. But 2/0,-5/0 are not RATIONALnumbers. MORE ABOUT RATIONAL NUMBERS PROPERTY NO- 1 Every natural number is a rational number but a rational number need not be a natural number. PROOF – We know that 1=1/1,2= 2 /1, 3= 3/1 and so on. Thus ,every natural number is a RATIONAL numbers. Clearly 3/2, 2/5 etc. are rational numbers but they are not natural numbers. Page 4 RATIONAL NUMBERS A number of the form P/Q or a number which can be expressed in the form P/Q ,where Pand Q are integers and Q not = 0 , is called a RATIONAL NUMBERS. EXAMPLE – Each of the numbers 2/3 , -5/7 ,-11/-5,7/-9 is a RATIONAL number. But 2/0,-5/0 are not RATIONALnumbers. MORE ABOUT RATIONAL NUMBERS PROPERTY NO- 1 Every natural number is a rational number but a rational number need not be a natural number. PROOF – We know that 1=1/1,2= 2 /1, 3= 3/1 and so on. Thus ,every natural number is a RATIONAL numbers. Clearly 3/2, 2/5 etc. are rational numbers but they are not natural numbers. PROPERTY- NO. 2 Zero is a RATIONAL NUMBER. PROOF-We know that the integer 0 can be written in any of the of the following forms :- 0/1, 0/-1, 0/2, 0/-2, 0/3, 0/-3, and so on. In other words ,0= 0/q, where q is non-zero integer. Thus 0 can be written as p/q ,where p=0 and q is any non-zero integer. Hence , 0 is a rational number. Page 5 RATIONAL NUMBERS A number of the form P/Q or a number which can be expressed in the form P/Q ,where Pand Q are integers and Q not = 0 , is called a RATIONAL NUMBERS. EXAMPLE – Each of the numbers 2/3 , -5/7 ,-11/-5,7/-9 is a RATIONAL number. But 2/0,-5/0 are not RATIONALnumbers. MORE ABOUT RATIONAL NUMBERS PROPERTY NO- 1 Every natural number is a rational number but a rational number need not be a natural number. PROOF – We know that 1=1/1,2= 2 /1, 3= 3/1 and so on. Thus ,every natural number is a RATIONAL numbers. Clearly 3/2, 2/5 etc. are rational numbers but they are not natural numbers. PROPERTY- NO. 2 Zero is a RATIONAL NUMBER. PROOF-We know that the integer 0 can be written in any of the of the following forms :- 0/1, 0/-1, 0/2, 0/-2, 0/3, 0/-3, and so on. In other words ,0= 0/q, where q is non-zero integer. Thus 0 can be written as p/q ,where p=0 and q is any non-zero integer. Hence , 0 is a rational number. PROPERTY NO. 3 Every integer is a rational number but a rational number need not be an integer. PROOF:- We can write 1= 1/1,2= 2/1, 3= 3/1and so on also –1= -1/1,-2=-2/1, -3= -3/1 and so on. Thus any integer p can be written as p= p/1, which is a rational number. So, integer is a rational number. Clearly 3/2,-5/3 etc. are rational numbers but they are not integers.Read More
FAQs on PPT: Rational Numbers
| 1. What are rational numbers? |  |
Ans. Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. They can be represented in the form of a fraction, such as 1/2, -3/4, or 5/7.
| 2. How do you identify if a number is rational? | |
Ans. To identify if a number is rational, we need to check if it can be expressed as a fraction of two integers. If it can be written in the form of p/q, where p and q are integers and q is not zero, then the number is rational.
| 3. Are whole numbers considered rational numbers? | |
Ans. Yes, whole numbers are considered rational numbers. Whole numbers are integers without any fractional or decimal parts. Since they can be expressed as fractions with a denominator of 1, they fall under the category of rational numbers.
| 4. What are examples of irrational numbers? | |
Ans. Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Examples of irrational numbers include √2, π (pi), and e (Euler's number). These numbers have decimal representations that neither terminate nor repeat.
| 5. Can rational numbers be negative? | |
Ans. Yes, rational numbers can be negative. Negative rational numbers are those in which the numerator is negative and the denominator is positive. For example, -3/5 and -7/8 are negative rational numbers.
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