Exercise 1.4

Question 1:

Without actually performing the long division, state whether the following rational numbers have a terminating decimal expansion or a non-terminating repeating decimal expansion.

i)233125

ii)2732

iii)32/35

iv)51600

v)2949

vi)2724×53

vii)2922×56×73

viii)315

ix)3550

x)77210

Solution :

Note; If the denominator has only factors of 2 and 5 then it has terminating decimal expansion.

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

i)233125=2352

Since, the denominator has only 5 as its factor, it has a terminating decimal expansion.

ii)2732=2725

Since, the denominator has only 2 as its factor, it has a terminating decimal expansion.

iii)3235=323×7

Since, the denominator has factors other than 2 and 5, it has a non-terminating decimal expansion.

iv)51600=526×52 =126×51

Since the denominator has only  2 and 5 as its factors, it has a terminating decimal expansion.

v)2949=2972

Since, the denominator has factors other than 2 and 5, it has a non-terminating decimal expansion.

vi)2724×53

Since the denominator has only  2 and 5 as its factors, it has a terminating decimal expansion.

vii)2922×56×73

Since, the denominator has factors other than 2 and 5, it has a non-terminating decimal expansion.

viii)315=15

Since, the denominator has only 5 as its factor, it has a terminating decimal expansion.

ix)3550=7×521×52 =721×51

Since the denominator has only  2 and 5 as its factors, it has a terminating decimal expansion.

x)77210=7×1121×51×3×7 =1121×51×3

Since, the denominator has factors other than 2 and 5, it has a non-terminating decimal expansion.

Question 2:

Write down the decimal expansion of the following rational numbers.

i)233125

ii)2732

iii)3235

iv)51600

v)2949

vi)2724×53

vii)2922×56×73

viii)315

ix)3550

x)77210

Solution;

i)233125=0.00736

ii)2732=.84375

iii)3235=.91428….

iv)51600=.00312

v)2949=.59183…

vi)2724×53=.0135

vii)2922×56×73=.00001…

viii)315=.2

ix)3550=.7

x)77210=.36¯

Question 3:

Decide whether the real numbers are rational or not. If they are rational, then write its pq form. What can you say about the prime factors of q?

i)24.1352436789

ii).12346783940564543……

iii)41.2¯

Solution;

i)24.1352436789

Since it has a terminating decimal expansion, it is a rational number and q has factors of 2 and 5 only.

ii).12346783940564543……

Since, it has non-terminating and non- repeating decimal expansion, it is an irrational number.

iii)41.2¯

Since it has a non-terminating but repeating decimal expansion, it is a rational number and q has factors other than 2 and 5 .


Exercise 1.1