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:
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.
Rough Workspace:
Example #2
A. 0.0144
B. 1.44
C. 14.4
D. 144
Correct Answer is: 0.0144 [Option A].
How to Solve: So, to find the missing value, we need to simplify the equation.
Firstly, let the missing value be
X.
So,
or,
or,
so,
finally,
Therefore, the missing value in this equation is,
0.0144.
Rough Workspace:
Example #3
Find the value of:
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.
Rough Workspace:
Example #4
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.
Rough Workspace:
Example #5
Arrange the fractions in their ascending order:
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
Rough Workspace:
Example #6
Find the value of:
(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.
Rough Workspace:
Example #7
Show Answer | Show How to Solve | Open Rough WorkspaceCorrect 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.
Rough Workspace:
Example #8
If 3x = 0.08y, then find the value of
Correct Answer is: [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
.
Rough Workspace:
Example #9
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.
Rough Workspace:
Example #10
What will be the difference between the biggest and smallest fraction among,
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.
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.