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:
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
A. 45
B. 55
C. 75
D. 100
Correct Answer is: 100 [Option D].
How to Solve:
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
So, to find out the value of this equation, we need to simplify the expression.
Firstly, we need to arrange it in such manner, so that we can apply math formula there.
So,
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
or, (4.5 x 4.5 + 2 x 4.5 x 5.5 + 5.5 x 5.5)
or, (a2 + 2ab + b2) where a=4.5 and b=5.5
so, (a + b)2 applying math formula
or, (4.5 + 5.5)2
or, (10)2
finally, 100
Therefore, the value of the given expression will be 100.
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
So, to find out the value of this equation, we need to simplify the expression.
Firstly, we need to arrange it in such manner, so that we can apply math formula there.
So,
(4.5 x 4.5 + 49.5 + 5.5 x 5.5)
or, (4.5 x 4.5 + 2 x 4.5 x 5.5 + 5.5 x 5.5)
or, (a2 + 2ab + b2) where a=4.5 and b=5.5
so, (a + b)2 applying math formula
or, (4.5 + 5.5)2
or, (10)2
finally, 100
Therefore, the value of the given expression will be 100.
Rough Workspace:
Example #2
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 #3
When 115611 is divided by 267, the quotient is 433. What will be the quotient if the decimal number 11.5611 is divided by another decimal number 0.433 ?
A. 2.67
B. 26.7
C. 267
D. 2670
Correct Answer is: 26.7 [Option B].
How to Solve:
So, to get the quotient value we need to divide the number.
Firstly, we know that,
or,
Now, the question asked is,
or,
or,
so,
or,
As we know that 
is equal to 267
or,
Therefore, the answer of the given question is 26.7.
So, to get the quotient value we need to divide the number.
Firstly, we know that,
or,
Now, the question asked is,
or,
or,
so,
or,
As we know that is equal to 267or,
Therefore, the answer of the given question is 26.7.
Rough Workspace:
Example #4
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 #5
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 #6
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 #7
Find the value of:
21.59 X 0.000001 = ?
21.59 X 0.000001 = ?
A. 0.00002159
B. 0.00021590
C. 0.00215900
D. 0.02159000
Correct Answer is: 0.00002159 [Option A].
How to Solve:
21.59 X 0.000001 = ?
So, here in this question we need to find the value of the given equation.
Actually this type of question solving is very easy. As you know that, in decimal multiplication we multiply the value only without the decimal places. And, after getting the multiplication result we add the decimal places and put it on the result.
So, here in this question, the values without decimal places are looks like,
2159 X 0000001
or, 2159 X 1
Therefore, the result of this multiplication would be, 2159.
Now, the decimal place of the first number is 2. And, the decimal place of the second number is 6. So, the sum of the decimal places are:
2 + 6
= 8
So, the result of the following equation 21.59 X 0.000001 is:
0.00002159
We add 8 decimal places to the multiplication result.
21.59 X 0.000001 = ?
So, here in this question we need to find the value of the given equation.
Actually this type of question solving is very easy. As you know that, in decimal multiplication we multiply the value only without the decimal places. And, after getting the multiplication result we add the decimal places and put it on the result.
So, here in this question, the values without decimal places are looks like,
2159 X 0000001
or, 2159 X 1
Therefore, the result of this multiplication would be, 2159.
Now, the decimal place of the first number is 2. And, the decimal place of the second number is 6. So, the sum of the decimal places are:
2 + 6
= 8
So, the result of the following equation 21.59 X 0.000001 is:
0.00002159
We add 8 decimal places to the multiplication result.
Rough Workspace:
Example #8
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 #9
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:
Example #10
What will be the difference between the biggest and smallest fraction among,
10/13, 15/19, 19/22, 23/26
10/13, 15/19, 19/22, 23/26
A. 1/13
B. 2/19
C. 3/22
D. 3/26
Correct Answer is: 3/26 [Option D].
How to Solve:
10/13, 15/19, 19/22, 23/26
So, to find out the difference between the biggest and smallest fraction, we need to convert every vulgar fraction into decimal.
Therefore, by converting every fraction into decimal we get,
10/13 = 0.769
15/19 = 0.789
19/22 = 0.863
23/26 = 0.884
So, now we can clearly say that,
0.769 < 0.789 < 0.863 < 0.884
or, 10/13 < 15/19 < 19/22 < 23/26
Therefore, the biggest fraction here is 23/26. And, the smallest fraction is 10/13.
Now, the difference between these two is,
or,
or,
So, the required answer of the given question is, 3/26.
10/13, 15/19, 19/22, 23/26
So, to find out the difference between the biggest and smallest fraction, we need to convert every vulgar fraction into decimal.
Therefore, by converting every fraction into decimal we get,
10/13 = 0.769
15/19 = 0.789
19/22 = 0.863
23/26 = 0.884
So, now we can clearly say that,
0.769 < 0.789 < 0.863 < 0.884
or, 10/13 < 15/19 < 19/22 < 23/26
Therefore, the biggest fraction here is 23/26. And, the smallest fraction is 10/13.
Now, the difference between these two is,
or,
or,
So, the required answer of the given question is, 3/26.
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.