Question

State which of the fraction 17/40 or 32/45 is terminating decimal without actual division and why?​

Answer 1

Answer:THE FIRST FRACTION(I.E. 17/40)IS TERMINATING FRACTION.

Step-by-step explanation:WE KNOW THAT,IF IN THE PRIME FACTORISATION OF THE DENOMINATOR,IF ONLY 2&5 APPEARS IN IT,THEN FOR SURE,THE FRACTION WILL TERMINATE AFTER SINGLE OR MULTIPLE DIGITS.HERE, LET'S TAKE THE FIRST FRACTION,THAT IS,17/40,HERE THE DENOMINATOR IS 40.SO LETS FACTORISE IT.40=2X5X2X2=2^3X5.SO HERE WE CAN EASILY SEE THAT ONLY 2 AND 5 APPEARS IN THE PRIME FACTORISATION OF THE DENOMINATOR OF THE FRACTION.HENCE,THE FIRST FRACTION,17/40 WILL TERMINATE AND HENCE IT IS A TERMINATNG FRACTION.HOPE U R HELPED.....PLEASE MARK MY ANS. AS BRAINLIEST AND GIVE IT A THANKS PLEASE.....

Answer 2

Answer:

The answer is $\frac{17}{40}$

While we are doing LCM for $\frac{32}{45}$ it is 5, 3, 3

and for $\frac{17}{40}$ it is 5, 2, 2, 2.

When there is 5 and 2 or just 5 (eg: 5,5,5) or 2 (eg: 2,2,2)

we know it is terminating

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