Quantitative Aptitude – Decimal Fraction
As we already discussed “What is Fraction“. A Decimal Fraction is one of the type of Fraction. It’s a basic and very common term in mathematics. A Decimal Fraction or popularly known as Decimal Numbers.
When we do math, most of the mathematical calculation is having decimal fraction in it. As we already says that it’s a basic thing in mathematics so you need to learn this chapter very carefully.
Now, let’s dig into the details of this topic.
What is Decimal Fraction ?
Basically, a Decimal Fraction is a combination of two numbers, one is Nominator and other is Denominator. The denominator of a decimal fraction is always a power of ten. And, the nominator represents the number of parts of denominator.
But, we don’t use decimal fraction in this format in our calculations (this rule is not applicable every time). We represent it in a more easier way by using a decimal point.
Few examples of Decimal Fractions:
- Suppose, 5/10 is a Fraction. So we represent it as 0.5 .
- Similarly, 5/100 can be represent as 0.05 .
Basically, the number of zeros in denominator is same as the number of digits in decimal places.
- So, in the first example 5/10, here 10 is a denominator which has only one zero. So, the decimal number must have minimum one digit in decimal places. Nominator of this fraction is 5, so, 5 will be added after the decimal point. So 5/10 is equal to 0.5 .
- And, in the next example, i.e, 5/100. Here denominator has two zeros. So the decimal number must have at least two digits in the decimal places. But, we have only one digit in nominator (5). So, here we have to add one extra digit after decimal point. And, we will add Zero to fill the gap. We add zero before the nominator. So, 5/100 is equal to 0.05.
So, you can add as much zeros as you want before a nominator, unless the number of digit in nominator will equals the number of zeros present in denominator.
Few Examples to Test your Decimal Fraction learnings:
Example #1
Find the value of:
A. 1
B. 2
C. 0.183
D. 3.728
Correct Answer is: 2 [Option B].
How to Solve:
So, to find the value of the given equation, we need to simplify it.
Firstly, we need to arrange it in such manner, so that we can apply mathematical formula there.
So,
or,
where, a = 3.728 and b = 0.183
or,
applying math formula
so,
finally,
Therefore, the value of the given equation is 2.
So, to find the value of the given equation, we need to simplify it.
Firstly, we need to arrange it in such manner, so that we can apply mathematical formula there.
So,
or,
where, a = 3.728 and b = 0.183or,
applying math formulaso,
finally,
Therefore, the value of the given equation is 2.
Rough Workspace:
Example #2
Find the missing value:
34.572 + 45.234 - ? = 11.522
34.572 + 45.234 - ? = 11.522
A. 68.284
B. 66.435
C. 69.317
D. 62.743
Correct Answer is: 68.284 [Option A].
How to Solve:
34.572 + 45.234 - ? = 11.522
So, to find the missing number in the following equation, we need to simplify the equation.
Let, the missing value be X.
then, 34.572 + 45.234 - X = 11.522
or, X = (34.572 + 45.234) - 11.522
or, X = 79.806 - 11.522
finally, X = 68.284
So, the missing value of the following equation is 68.284.
34.572 + 45.234 - ? = 11.522
So, to find the missing number in the following equation, we need to simplify the equation.
Let, the missing value be X.
then, 34.572 + 45.234 - X = 11.522
or, X = (34.572 + 45.234) - 11.522
or, X = 79.806 - 11.522
finally, X = 68.284
So, the missing value of the following equation is 68.284.
Rough Workspace:
Example #3
Find the product:
.7 x .07 x .007 x 70
.7 x .07 x .007 x 70
A. 0.024010
B. 0.049000
C. 0.077770
D. 0.000070
Correct Answer is: 0.024010 [Option A].
How to Solve:
.7 x .07 x .007 x 70
So, in this example we need to multiply every decimal values.
Firstly, we need to take off all the decimal places. And, multiply only the whole numbers.
So, here the equation becomes,
7 x 7 x 7 x 70
= 24010
Now, we need to add all the decimal places and put it into the multiplication result.
So, the sum of all decimal places are:
1 + 2 + 3 + 0
= 6
Finally, the result of the following equation after adding decimal places is, 0.024010.
.7 x .07 x .007 x 70
So, in this example we need to multiply every decimal values.
Firstly, we need to take off all the decimal places. And, multiply only the whole numbers.
So, here the equation becomes,
7 x 7 x 7 x 70
= 24010
Now, we need to add all the decimal places and put it into the multiplication result.
So, the sum of all decimal places are:
1 + 2 + 3 + 0
= 6
Finally, the result of the following equation after adding decimal places is, 0.024010.
Rough Workspace:
Example #4
If 
, then find the value of 
.
, then find the value of .A. 61X
B. 10X
C. X/10
D. 341632X
Correct Answer is: X/10 [Option C].
How to Solve:
So, to find the value of, we need to arrange the equation in such manner so that we can apply the value of X in it.
Therefore,
or,
or,
now,
or,
As 
or,
So, the value of is .
So, to find the value of
, we need to arrange the equation in such manner so that we can apply the value of X in it.Therefore,
or,
or,
now,
or,
As or,
So, the value of
is .Rough Workspace:
Example #5
Find the missing value:
A. 3.36
B. 13.28
C. 16.64
D. 20
Correct Answer is: 13.28 [Option B].
How to Solve:
So, to find the missing value we need to simplify the expression and apply mathematical formula in it.
Firstly, arrange the equation as mathematical form.
So,
or,
let, the missing number be X.
or,
so,
or,
where a=16.64 and b=3.36
or,
applying the formula of (a2 - b2)
so,
or,
finally,
Therefore, the missing number here in this equation is, 13.28.
So, to find the missing value we need to simplify the expression and apply mathematical formula in it.
Firstly, arrange the equation as mathematical form.
So,
or,
let, the missing number be X.or,
so,
or,
where a=16.64 and b=3.36or,
applying the formula of (a2 - b2)so,
or,
finally,
Therefore, the missing number here in this equation is, 13.28.
Rough Workspace:
Example #6
Arrange the fractions in their ascending order:
3/5, 2/9, 5/8, 1/3
3/5, 2/9, 5/8, 1/3
A. 3/5 < 5/8 < 2/9 < 1/3
B. 5/8 < 2/9 < 3/5 < 1/3
C. 2/9 < 1/3 < 3/5 < 5/8
D. 5/8 < 3/5 < 1/3 < 2/9
Correct Answer is: 2/9 < 1/3 < 3/5 < 5/8 [Option C].
How to Solve:
3/5, 2/9, 5/8, 1/3
So, in this example we need to find out the decimal fraction of every value. And, then compare the decimal value with every other fraction.
So, Decimal fraction of these fractions are:
3/5 = 0.600
2/9 = 0.222
5/8 = 0.625
1/3 = 0.333
Therefore, from the decimal value we can clearly arrange these fractions into their ascending order-
2/9 < 1/3 < 3/5 < 5/8
3/5, 2/9, 5/8, 1/3
So, in this example we need to find out the decimal fraction of every value. And, then compare the decimal value with every other fraction.
So, Decimal fraction of these fractions are:
3/5 = 0.600
2/9 = 0.222
5/8 = 0.625
1/3 = 0.333
Therefore, from the decimal value we can clearly arrange these fractions into their ascending order-
2/9 < 1/3 < 3/5 < 5/8
Rough Workspace:
Example #7
Find the value of:
7.81 X 105 = ?
7.81 X 105 = ?
A. 781
B. 7810
C. 78100
D. 781000
Correct Answer is: 781000 [Option D].
How to Solve:
7.81 X 105 = ?
So, in this question we need to simplify the equation and find the value of it.
So, 7.81 X 105
= 7.81000 X 100000
= 781000
So, the value of the equation 7.81 X 105 is 781000.
7.81 X 105 = ?
So, in this question we need to simplify the equation and find the value of it.
So, 7.81 X 105
= 7.81000 X 100000
= 781000
So, the value of the equation 7.81 X 105 is 781000.
Rough Workspace:
Example #8
If 3x = 0.08y, then find the value of 
A. 
B. 
C. 
D. 
Correct Answer is: [Option A].
[Option A].How to Solve:
So, to find the value of the given equation, we need to simplify it.
Firstly, as we know that, 3x = 0.08y.
So,
or,
or,
Now, to find the value of the given equation we will apply the value of
So,
or,
or,
putting the value of x/y
so,
or,
finally,
Therefore, the value of the given equation is.
So, to find the value of the given equation, we need to simplify it.
Firstly, as we know that, 3x = 0.08y.
So,
or,
or,
Now, to find the value of the given equation we will apply the value of
So,
or,
or,
putting the value of x/yso,
or,
finally,
Therefore, the value of the given equation is
.Rough Workspace:
Example #9
Find the value of:
A. 350
B. 400
C. 500
D. 600
Correct Answer is: 500 [Option C].
How to Solve:
So, to find the value of the given equation we need to simplify the equation.
Therefore,
=
=
So, the value of the given equation is 500.
So, to find the value of the given equation we need to simplify the equation.
Therefore,
=
=
So, the value of the given equation is 500.
Rough Workspace:
Example #10
A plumber has 37.5 meter pipes. He has to cut 8 small pipe pieces with every 1 meter pipe. So, how many small pipes can he cut out of the entire pipe.
A. 225
B. 250
C. 275
D. 300
Correct Answer is: 300 [Option D].
How to Solve:
So, in this question we need to find the total number of small pipe pieces.
And, according to the question we can say that,
Length of each pipe:
1/8 meter
or, 0.125 meter.
Therefore, the required number of pipes are:
37.5 / 0.125
= (375 X 100) / 125
= 300
So, he can cut total 300 small pipe pieces with the entire 37.5 meter pipe.
So, in this question we need to find the total number of small pipe pieces.
And, according to the question we can say that,
Length of each pipe:
1/8 meter
or, 0.125 meter.
Therefore, the required number of pipes are:
37.5 / 0.125
= (375 X 100) / 125
= 300
So, he can cut total 300 small pipe pieces with the entire 37.5 meter pipe.
Rough Workspace:
So, if you need any farther help on this chapter, then please let us know. And, surely We will discuss on those problems here in www.AptitudeTricks.com.