Question

without actual division division determine whether 21/56has a terminating decimal representation or not​

Answer 1

A fraction is terminating only if the denominator have just the factors which are exponents of 2 or 5 or both in lowest term of fraction


So here ,
First reduce the fraction in its lowest term
Here 56 has a factor 7 , 8
And 21 have factors 7,3

So if you divide both the pats of fraction by seven then simply your fraction will be reduced to its lowest form ,

After reduction you will have 3/8


Now the denominator satisfies the conditions of being terminated , so 3/8 is terminating , so 21/ 56 will also be terminating


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But 21 also