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
recurring.
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.

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  • Q1

    1.44 is

    Marks:1
    Answer:

    a rational number.

    Explanation:

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  • Q2

    A decimal number 25.75 can be written as

    Marks:1
    Answer:

    103/4

    Explanation:

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  • Q3

    Decimal form of 1257/125 is

    Marks:1
    Answer:

    10.0560

    Explanation:

    Since,

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  • Q4

    Decimal form of 37/13 is

    Marks:1
    Answer:

    Explanation:

    37/13 = 2.8461538461538461538461538… =

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  • Q5

    Two rational numbers between 0.1212212221… and 0.2323323332… are

    Marks:1
    Answer:

    0.221 and 0.222.

    Explanation:

    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…

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