# CLASS-9TERMINATING DECIMAL

We shall learn the idea of terminating decimals below.

Terminating Decimals

In order to express a fraction x/y in decimal form, we divide ‘x’ by ‘y’. If after a finite number of steps, no reminder is left, then we call it a terminating decimal.

For example –

1                       3                         34

a) ------ = 0.50,   b) ------- =  0.375c) -------- = 6.8

2                       8                          8

are all terminating decimals.

An important result, a fraction x/y would be considered as a terminating decimal only when prime factors of ‘y’ are out of 2 & 5 only.

Example.1)  Without actual division, find out, which of the following fractions are terminating decimals.

a)   11/20

Ans.)  The given number is 11/20 and HCF of (11, 20) = 1

so, 11/20 is in simplest form.

now, 20 = 2 X 2 X 5

so, the prime factors of 20 are 2 & 5. Hence 11/20 is a terminating decimal

b)    43/60

The given number is 43/60 and HCF (43, 60) = 1

so, 43/60 is in the simplest form.

Now, 60 = 2 X 2 X 3 X 5

Thus the prime factors of 60 are 2, 3, and 5

Hence, 43/60 is a non-terminating, repeating decimal.

c)    66/180

the given number is 66/180 and HCF (66, 180) = 6

66           66 ÷ 6            11

so, -------- = ------------ = --------

180          180 ÷ 6           30

Thus, 11/30 is simplest form. Now, 30 = 2 X 3 X 5

So, the prime factors of 30 are 2, 3, and 5

Hence, 11/30 and hence 66/180 is non-terminating, repeating decimals.

d)   121/252

the given number is 121/252 and HCF (121, 252) = 1

so, 121/252 is in simplest form.

Now, 252 = 2 X 2 X 3 X 3 X 7

Thus, the prime factors of 252 are 2, 3, and 7.

Hence, 121/252 is a non-terminating, repeating decimals.