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.

I didn't understand the concept behind 0.1250 =125/1000.

Anyone, please explain

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.

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 1/6, 2/3, 5/6 come? Please explain.

How the simplification is done?

I'm not able to understand. Please explain this in detail.

How it becomes 3333/2222 to 3/2? Pleas tell me.

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.

According to vulgar fractions;

If given 0.1666 = (16 - 1)/90 = 15/90 = 1/6.

But here 0.1667 so can we consider it as 0.1666.