Question

Express the following in decimal form.
(i) 7/5, 3/4, 23/10, 5/3, 17/6, 22/7
(ii) Which of the above are terminating and which are non-terminating decimals ?
(iii) Write the denominators of above rational numbers as the product of primes.
(iv) If the denominators of the above simplest rational numbers has no prime divisors other than 2 and 5 what do you observe?

Answer 1

(1) (i)1.4,(ii)0.75,(iii)2.3,(iv)1.66666...,(v)2.83333....,(vi)3.142857....
(2)7/5 , 3/4 and  23/10 are terminating while 5/3 , 17/6 and 22/7 are non terminating decimals.
(3)5=5 (a single prime) , 4=2*2 , 10=2*5.
(4) If the denominators of the simplest fractions have no prime divisors other than 2 and 5, then the fraction takes form of a non-terminating or recurring decimal.

Answer 2

express the following in decimal form of 3/4