Page 77 - Maths Skills - 7

Rational Numbers 75

DECIMAL NUMBER AS RATIONAL/IRRATIONAL NUMBER
We have learnt how to convert a fraction into a decimal and a decimal into a fraction. Consider the rational
2
number . To convert this into a decimal form, we divide 2 by 5.
5 0.75
2 0.4 3
Therefore, = 0.4 Similarly, the decimal form of is 0.75. 4 30
5 5 20 4 28
20 20
0 20
0

13 3
The decimal form of is 2.6 and is 0.375. In all the cases discussed here, the number of digits after the
5 8
decimal point is finite. Such decimals are called terminating decimals.

2 1 11
Now, consider the rational numbers: , , .
3 6 9
Let us find the decimal equivalent of these rational numbers.

0.666...
2 ⇒ 3 20 The division process is non-ending, as number 6 will repeat
3 18 without terminating. Such decimals are called non-terminating
20 or repeating decimals. 2
2
18 So, we express = 0.666... or = 0.6
20 3 3
18 [The bar above the number 6 shows that it repeats endlessly.]
20

1
Now, we consider 1
6 Here, only number 6 repeats. So, the decimal form of can be
0.1666... 1 6
6 10 written as = 0.16666... or 0.16.
6
6 [The bar is only for 6 as the digit 6 repeats endlessly.]
40 By seeing the above examples we can conclude that those
36
40 decimals which are terminating or repeating called rational
numbers.
36
40 But those decimal which are non-terminating and non-repeating
36 called irrational numbers.
40 For example, the value of p = 3.14159265359......... which is non-
terminating and non-repeating. So p is irrational number.