Question

how to tell if a fraction is terminating or repeating

Answer 1

if the denominator of the fraction is in the form of2^m*5^n it is terminating or else it is repeating .

Answer 2

hello friend!

good morning..

first of all, what are terminating numbers and how can you tell that this fraction is terminating..

for example take 1/7 and the decimal expansion of 1/7 is 0.1428142.... in this case, the decimal expansion never ends and remainder never comes zero. so it's not a terminating.

now, take example 1/2 if you do it's decimal expansion, the final answer will be 0.5 and it's decimal expansion terminates after some steps and final remainder comes 0. such fractions are called terminating. in short we can say that whose remainder becomes zero atleast are terminating.

now, there are two tyyof non-terminating numbers..

one is repeating and another one is non-repeating.

take example 1/3 and it's decimal expansion = 0.3333333.... and "3" is repeating in this case.

another example 1/7 = 0.124857142857...

in this case "124857" is repeating, so this is also a repeating number.

when a digit or a block of digits continuously repeats in a decimal expansion are called repeating numbers.

now, 0.62749351836351826362816354...

the digits are repeating?

we can clearly see that no number is repeating. such decimal expansion are called non - repeatig.

hope you understood and if any doubts, you can comment below.



and one more thing, terminating and repeating numbers are rational numbers and non-terminating non-repeating numbers are irrational numbers.