Aptitude - Decimal Fraction - Discussion

Hey everyone.

Someone is confused about how we get to the place of.

(0.1667), (0.8333), (0.2222), (0.6667), (0.1250) we get 1/6, 5, 6, 2/3, 125/100.

Let me explain;

Here; They ask approx value so we consider 0. 1667 as 0. 1666 and by converting it into a fraction we get 1/6.

Calculation part;

0.1666 as 0. 16 where 6 has a bar on it.
0.16. = 16/90 = 1/6.

Similarly, 0. 8333 consider 0. 83 and 3 has a bar on it.

Calculation part ;

0.83. = 83 - 8 /90 = 75/90 = 5/6.

Similarly, consider 0. 6667 as 0. 6666 solving it we get 2/3.

Calculation part;

0.6. = 6/9 = 2/3.

Hear 0.1250 as 0.124 solving it we get 125/100.

Here is the thing.

x = .8333 can be converted as 100x = 83.3333 and 10X = 8.3333, and why so because we need to focus on how many decimals are recurring here it's just one(3) and so we need to remove that.
Always put recurring part behind the decimal (here by multiplying with 10) .and this way the result comes out to be 83 - 8/90 = 75/90 = 5/6 and 0.1250 = 125/1000 = 1/8.

it's basically a bar concept. That is 0.22222 can be written as 0.2 and infraction it can be written as 2/9.

The formula is (number without decimal - non-repeating numbers)/put 9's the number of repeating numbers and 0's the number of non-repeating numbers.

Suppose, 0.35232323 it can be written as (3523 - 35)/(9900).
Put that in that problem and you are good to go.

For getting 0.16667 as 1/6, we can do:

0.1667*10 = 1.6667.

Now, 1.6667 is equal to 1+ 0.6667, we know how to convert 0.6667 to a fraction.
0.6667 = 6/9 => 2/3.

Therefore, we have 1+ 0.667 => 1+(2/3)=> 5/3,

But remember we multiplied by 10 in the beginning, so we divide by 10 to nullify the change.
Therefore (5/3)/10 => 1/6.

Here is a solution:

0.1667 = 0.1666 ; 0.16 (6-bar) ; (16-1)/90 = 1/6.
0.8333 = 0.83 (3-Bar); (83-8)/90= 75/90 = (5/6).

0.3333 = 0.3 (3-bar); (3/9) = 1/3.
0.2222 = 0.2 (2-bar); (2/9).
0.6667 = 0.6 (6-bar); 6/9 = 2/3.
0.1250 = 1/8.

Substitute at the given places and get the answer as 2.50.

Study Conversion of Recurring Decimals.

In simple words for recurring decimals keep recurring values behind the decimals and assume it as your starting point.

X=.83333 so let's assume Z= 8.3333 and you know Z=10X ,and now solve Z and you will get Z = 75/9.

And later you can solve for X which will be 10X = 7.5/9 or X = 75/90.

Guys i've found a simple method.
u can covert it like x=.1667 and 10x=1.667=>9x=1.5003 so x=1/6
similarly for y=0.6667=> y=2/3
and 0.8883=1-0.1667=>1-1/6=5/6
now it's easy method to solve this problem.

hope,it will help u to solve this problem.

Hi all, from my understanding, the conversion to a fraction is actually used for non-terminating recurring decimals, however, that is not the case here, all are terminating decimals, we can convert them only like, 0.67 = 67/100.

All are multiplied by 10000 so that they can become whole numbers.

Take the first two digits 16*83*33=43824.
Take denominator first two digits 22*66*12=17424.
So, 43824/17424 = 2.51.

How you pupil take that 0.1667 as 0.16 bar because in question they gave only 0.1667 but not 0.166666666.

Then how recurring works? Please can any one explain me.