# Aptitude: Decimal Number Problems

## Formula:

Converting pure recurring decimal into simple fraction:

In order to convert into simple fraction, we write the repeated figures only once in the numerator without decimal point and write as many nines in the denominator as the number of repeating figure.

Converting mixed recurring decimal into simple fraction:

In this numerator is obtained by taking the difference between the number formed by all the digits after decimal point.and the number formed by non-repeating digits.the denominator is obtained by placing,as many nines as in repeating digits followed by as many zeroes as the number of non-repeating digits

Note: In this text underline is referred as bold letters

The vulgar fraction of 0.1236 is

= (1236 – 12) / 9900

= 1224/9900

= 102/825

What is the value of 1.34 + 4.12 ?

1.34 = 134 – 1 / 99

= 133 / 99

4.12 = 412 – 41 / 90

= 371/90

So, 133 / 99 + 371 / 90 = 1330 + 4081/990

= 5411 / 990

Arrange 7/8, 5/6 , 6/7 in descending order

By taking the LCM of 8, 6, 7 = 168 and making every denominator equal we get 147/168, 140/168, 144/168.

Here the descending order is 140/168 < 144/168 < 147/168

So 7/8, 6/7, 5/6 is the order.

When 0.232323… is converted into a fraction, then the result is

By using the method specified above we can write it as => 23/99

If 2.5252525.. = p/q, then what is the value of q/p?

As 2.525252.. can be written as => 252-2/99 in simple fraction

Then q/p = 99/250 =>  0.396

What is the value of 0.0077777… + 17.8383838… + 310.02022222… ?

By adding all these numbers we get

= 327.866383838…

Note: we can add directly recurring decimal but in subtraction we first have to   convert them into a simple fraction before doing subtraction on them.

Simplify 0.636363… -  0.373737…

Let x = 0.6363636… =>  x = 63/99

Similarly other term y = 37/99

x-y = 63/99 – 37/99 = 26/99 = 0.262626…

7.2 exceeds its one-tenth by

7.2 – 7.2/10 => 7.2 – 0.72 = 6.48.(this que is easy if you understand the  language properly)

If the points P and Q represent the real numbers 0.81111… and 0.633333… on the number line, then the distance between P and Q is

P can be written as = 81 – 8 / 90 and similarly Q = 63 – 6 / 90

Now P-Q = 73/90 – 57/90 = 16/90 = 0.17777…