Real Numbers and its Properties
The real numbers include all the rational and irrational numbers.
There is a real number corresponding to each point on the number line and vice versa.
The decimal expansion of a rational number is either terminating or non-terminating
The sum, difference and product of a rational and an irrational number is always an irrational number. Also, when an irrational number is divided by a rational number then the quotient is an irrational number.
The sum, difference, quotients and products of irrational numbers are not always irrational.
For any non-zero real number ‘a’ and a positive integer ‘n’, a–n =1/an.
If a, b are any real numbers and m, n are any positive integers, then
(i) a0 =1 (ii) am × an = am+n (iii) am/ an = am–n (iv) (am)n= amn = (an)m (v) (ab)n= an bn
(vi) (a/b)n= an/ bn, b ? 0.
Keywords: Real Numbers and their Decimal Expansions
Real Numbers and Their Properties, Representing Real Numbers on a Number Line, Laws of Exponents for Real Numbers, Operations on Real Numbers.
To Access the full content, Please Purchase
a rational number.
A decimal number 25.75 can be written asMarks:1
Decimal form of 1257/125 isMarks:1
Decimal form of 37/13 isMarks:1
37/13 = 2.8461538461538461538461538… =
Two rational numbers between 0.1212212221… and 0.2323323332… areMarks:1
0.221 and 0.222.
Since numbers 0.221 and 0.222 both are terminating decimal numbers, therefore 0.221 and 0.222 will be two required rational numbers between 0.1212212221… and 0.2323323332…