Do you know simple way to change decimal to fraction?

[reza_moohebat]

Hello everybody,

I have started my study program recently with this website. I saw a question which seems difficult at first. look at the question:

(1.3333)(0.666)(1.125)
__________________
(0.75)(0.8)(0.8333)

some decimals are simple and we can covert them to fractions quickly, but some of them like (1.3333) and (0.666) or (0.83333) seems complicated. The solution says we should convert it in this way:

(4/3)(2/3)(9/8)
_____________=2
(3/4)(4/5)(5/6)

now, my question is how we can calculate quickly that the fraction in form of (0.8333) is (5/6) or (1.3333) is (4/3) and etc?

Thanks

[amising6]

see i would suggest you by heart the fraction from 1/2 to 1/15
then you would have to aplly your learning
we know 1/3=0.3333
so if o.6666 you know this is equal to 2*0.3333 so this is 2/3
similairly you know 1/6=.16666666 so if you get 0.333332 you should know this is 2/6

[reza_moohebat]

see i would suggest you by heart the fraction from 1/2 to 1/15
then you would have to aplly your learning
we know 1/3=0.3333
so if o.6666 you know this is equal to 2*0.3333 so this is 2/3
similairly you know 1/6=.16666666 so if you get 0.333332 you should know this is 2/6

Thanks, do you suggest we remember some fractions and try to built other factions with them? How do you convert for example 0.8333 or 1.125? can you explain more my friend?

Thanks.

[uwhusky]

Absolutely, I think there are some basic fractions worth memorizing.

[reza_moohebat]

Hi guys. I found the solution finally. You do not need to remember anything. It has two formula.

If we have decimal with simple repetition part like 0/3333, 4/545454 we should use this one:

(whole the number without /)-(the number before /)
_________________________________________
put 9 instead of numbers of repetition part

example: 454-4
______
99

If we have compound decimal like 0/67777 or 0/83333, we should use this one:

(whole number without /) - (the number without repetition part)
____________________________________________________

put 9 instead of repetition part * 10(numbers of non repetition part after /)


example:
0/833333=83-8
____
9*10
and finally we have 75/90 and it means 5/6



this way is more practical than memorizing isn't it?

[uwhusky]

I don't follow...

Oh I get it. You're using very different expressions than what I am used to.

Sure, your method works, but personally I think it's easier to memorize simple fractions than to memorize another equation. Plus your equation still needs to be simplified, and that's also more work.

[reza_moohebat]

Absolutely, I think there are some basic fractions worth memorizing.

What is your personal method to solve this question? What fractions do you memorize? For GMAT quickest is better.