Maths : Real Numbers : Points to Remember

**Maths: ****Real Numbers**

**Points to Remember**

•
When the decimal expansion of *p*/*q* , q≠0 terminates that is, comes to an end,
the decimal is called a terminating decimal.

•
In the decimal expansion of *p/q* , q≠0
when the remainder is not zero, we have a repeating (recurring) block of digits
in the quotient. In this case, the decimal expansion is called non-terminating and
recurring.

•
If a rational number *p/q* , q≠0 can be
expressed in the form , where p ∈ Z and *m*,* n *∈ W, then the rational number will have a terminating decimals.
Otherwise, the* *rational number will have a non-terminating repeating (recurring)
decimal.

• A
rational number can be expressed either a terminating or a non- terminating recurring
decimal.

• An
irrational number is a non-terminating and non-recurring decimal, i.e. it cannot
be written in form *p/q* , where p and q are both integers and q ≠ 0.

• The
union of all rational numbers and all irrational numbers is called the set of real
numbers.

• Every
real number is either a rational number or an irratonal number.

• If
a real number is not rational number, then it must be an irrational number.

• If ‘*a*’
is a positive rational number, ‘*n*’ is a positive integer and if * ^{n}*√

•
If ‘*m*’, ‘*n*’ are positive integers and *a*, *b* are positive
rational numbers, then

(i)
(* ^{n}*√a)

•
The process of multiplying a surd by another surd to get a rational number is called
Rationalisation.

• Expressing
a number *N* in the form of *N* = *a* ×10* ^{n}*
where, 1 ≤

Tags : Real Numbers | Maths , 9th Maths : UNIT 2 : Real Numbers

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9th Maths : UNIT 2 : Real Numbers : Points to Remember | Real Numbers | Maths

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