Question

Question about decimals

I have a math problem
205.17/713.95
I worked it out all by hand and eventually got to 34.79797241 as the calculator stated. This problem was very time consuming as it took a lot of work to complete. I was wondering if there was a simpler way of cutting my answer short that would also be correct?. I am unable to determine if this number is terminal or repeating as the decimal answer looks repeating with the 7979 but then appears to be terminal with the 241 part. Im assuming this number is terminal? Do I just need to suck it up and do the math or Is there a certain part of the decimal place value it would be appropriate to just stop at?


One more question unrelated to my previous questions.
I originally tried to solve this problem out of (A.) 713.95the divisor /by 205.17 the dividend as I know I am ALWAYS supposed to put the bigger number in the dividend section, but I am curious on how I would go about solving this question the opposite way (B.) with 205.17 as the divisor /by 713.95 as the dividend. I know this is possible as the calculator states
(A.) 713.95/205.17 =3.479797241
(B.) 0.2873730653 (I'm guessing this overwhelmingly long decimal is also terminal?)

Answer 1

• Both are terminating decimals

Explanation:

Answer to your questions:

• First of all, both A and B are correct and both quotients are terminating decimals.

• To find out if the decimal is terminating or not, multiply the quotient by divisor. If you get exactly the same number as dividend, then it is terminating otherwise it is non-terminating.

• The fraction may have greater numerator than denominator, in this case the quotient will be greater than one.
• Now regarding simplification. You would be asked to give an answer rounded to some extend. One decimal place, two decimal places, 3 significant numbers etc. For the first operation you would get 34.8 (rounded to nearest tenth).
• Or you may be asked to have a best estimated result. In this case you would round the initial numbers and find results. 205/714 ≈ 0.29