Page 30 - SM inner class 7.cdr

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be written as = 03333. During this Note :
.
3 1. A decimal in which all the digits after
process, the digit 3 is repeated again and
the decimal point are repeated, is called
again. To express their fact a bar or dot is a pure recurring decimal
placed over the repeating digit.
1 · For ex am ple : 0 3 0 6 016. , . , . , etc
.
.
Thus, = 03333 = 0 3 or 0 3 2. A decimal in which at least one digit
.
3
after the decimal point is not repeated
1
.
.
(ii) Similarly, we find that = 016666 = 016 besides having some repeated digits, is
6 known as a mixed recurring decimal.
·
or 016. . It is deduce that the division never For ex am ple : 0 13 0416 0185. , . , . , etc.
comes to an end and a digit or a block of
digits repeats itself again and again. During the decimal representation of the
These are called non-ter mi nat ing and above rational number, it is observed that the
re peat ing dec i mals. division never comes to an end and a digit or a
block of digits repeats itself again and again.
Similarly, we find that
1 These are called non-terminating and
= 01111..... = 0 1 repeating decimals.
.
.
9
3 Now, study the following :
= 0272727..... = 0 27
.
.
11
2
= 0285714285714285714......
.
7
= 0 285714
.
5
= 08333 = 0 83
.
.
6
Ra tio nal Num ber and their Equiv a lent De nom i na tor Prime Fac tors
Dec i mal Rep re sen ta tion
1
.
(= 05) 2 2
2
1
(= 025) 4 2, 2
.
4
1
(= 02) 5 5
.
5
1
.
(= 0125) 8 2, 2, 2
8
3
(= 012) 25 5, 5
.
25
8
(= 0064) 125 5, 5, 5
.
125
151
.
(= 3775) 40 2, 2, 2, 5
40
We find that—in each of the above cases, the Ex am ple 22. With out ac tual di vi sion de ter mine
prime factors of the denominator are only 2 or which of the fol low ing ra tio nal num bers have a
5 or both and their equivalent decimal ter mi nat ing dec i mal representation :
representations are all terminating. 19 23
(i) (ii)
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Mathematics In Focus - 7