# Decimal Fraction Formulas

In competitive exams such as Banking, Railway, Defense UPSC, SSC and other question from Decimal Fraction topics from will be asked to test the aptitude skills of participants. So, check Decimal Fraction Formulas as well as Aptitude Tricks to qualify this section with good scores.

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Decimal Fraction Important Formulas

Applicants who are going to appear for any competitive exams and find difficulty during solving decimal fraction questions then must check Decimal Fraction Important Formulas and Tricks to avoid any mistake. Also go through Decimal Fraction Practice Problems to get familiarize with type of question asked in exam

Aptitude Decimal Fraction Formulas and Tricks

Here in this article, we team of recruitmentresult.com decimal fraction Tricks and formula with examples which will help you to improve performance. You can learn decimal fraction formula and also practice of decimal fraction questions and answers.

## Decimal Fraction Formulas

What is Decimal Fraction?

A decimal fraction is a fraction in which denominator is an integer power of ten. A decimal fraction is expressed using decimal notation and its denominator is not mentioned explicitly. (Term decimals is commonly used to refer decimal fractions).

Examples:

110110 = .1
11001100 = .01
1710017100 = .17
410000410000 = .0004
121100121100 = 1.21

Decimal fractions can also be expressed using scientific notation with negative exponents. Example: 4.193 × 10−7 is a decimal fraction which represents .0000004193

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How Can I Convert Decimal Into Vulgar Fraction?

Put 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

Thus, 0.25 = 25/100= ¼
2.008 =2008/1000 = 251/ 125

Annexing Zeros and Removing Decimal Signs

Annexing zeros to the extreme right of a decimal fraction does not change its value. Thus, 0.8 = 0.80 = 0.800, etc. If numerator and denominator of fraction contain same number of decimal places, then we remove the decimal sign.

Thus, 1.84/2.99 = 184/299= 8/13

Comparison of Fractions

Suppose some fractions are to be arranged in ascending or descending order of magnitude, then convert each one of the given fractions in the decimal form, and arrange them accordingly.

 Let us to arrange the fractions 3 , 6 and 7 5 7 9

 Now, 3 = 0.6, 6 = 0.857, 7 = 0.777… 5 7 9

 Since, 0.857 > 0.777… > 0.6. So, 6 > 7 > 3 7 9 5

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Recurring Decimal Fractions

If a figure or set of figures is repeated continuously, such a number is called a recurring decimal. If single figure is repeated, then it is expressed by putting dot but If a set of figures is repeated, it is expressed by putting a bar on the set.

1/3 = 0.333 =0.3

22/7= 3.142857142857…. = 3.142857

Pure Recurring Decimal

A decimal fraction, in which all the figures after the decimal point are repeated, is called a pure recurring decimal
Such as 0.5 = 5/9; 0.53 = 53/59 ;0.067 = 67/999;

Mixed Recurring Decimal:

A decimal fraction in which some figures do not repeat and some of them are repeated is called a mixed recurring decimal
such as 0.17333= 0.173.

How to Convert Mixed Recurring Decimal Into Vulgar Fraction?

In numerator, take difference between numbers all the digits after decimal point. In denominator, take number formed by as many nines as there are repeating digits followed by as many zeros as is the number of non-repeating digits.
0.16 = (16-1) / 90 = 15/19 = 1/6

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Operations on Decimal Fractions

Addition and Subtraction of Decimal Fractions

Place given numbers under each other so that decimal points lie in one column. Now  arranged numbers to add or subtrac in the usual way.

Multiplication of Decimal Fraction By Power of 10

Shift decimal point to the right by as many places as is the power of 10.
Thus, 5.9632 x 100 = 596.32;   0.073 x 10000 = 730

Multiplication of Decimal Fractions

Multiply numbers considering them without decimal point. Now, mark decimal point in the product to obtain as many places of decimal

Suppose, Find the [product (.2 x 0.02 x .002).
Now, 2 x 2 x 2 = 8
Sum of decimal places = (1 + 2 + 3) = 6.
.2 x .02 x .002 = .000008

Dividing a Decimal Fraction By a Counting Number

Divide the given number without considering the decimal point, by the given counting number. Now, in the quotient, put the decimal point to give as many places of decimal as there are in the dividend.

Suppose we have to find the quotient (0.0204 ÷ 17). Now,  204 ÷ 17 = 12.
Dividend contains 4 places of decimal. So, 0.0204 ÷ 17 = 0.0012

Dividing a Decimal Fraction By a Decimal Fraction

Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number. Now, proceed as above.
Thus,0.00066/0.11 = (0.00066*100)/(0.11*100) = (0.066/11) = 0.006V

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Decimal Fraction Solved Examples

Example1:- Evaluate the following – i) 6.4209××100  ii)0.0379××10

Solution:

1) 6.4209××100 = 642.09

• 2) 0.0379××100 = 0.379Multiply a decimal fraction by a power of 10,
• Shift the decimal point to the right by as many places of decimal as is the power of 10.
• Multiplication of two or more decimal fraction.

Example 2:- Find the productions of the following –

1)2.257××2.1
2) 2.79×× 1.31
3) 5××0.5××0.0005

Solution:

(1) 2.257 ××2.1 = 4.7397
Sum the decimal place = (3 + 1) = 4

Now put the decimal after 4 that counting 4 digits from right thus 4.7397 is answer.

(2) 2.79 ××1.31 = 3.6549

Multiplied 279 and 131 results is 36549. Total decimal places are 4, put decimal counting four digits from right.

(3) 5 ××0.5××0.05××0.0005 = 0.0000625

Multiplied 5, 4 times, get 625, now number of decimal places are 7, so place 4 zeros on left of 625 and then mark decimal. Decision of decimal fraction by a non-zero whole number

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Example 3: Evaluate the following – (1) 0.72 + 9 (2) 0.0625 + 5

Solution:

1) 0.72 + 9 =0.7290.729=0.08
(Divided 72 by 9, get 8 as result now count decimal places in 0.72 that is ‘2’, hence place the decimal point on left of 08 that is, 0.08)

2) 0.062550.06255=0.0125
(Divided 625 by 5, get 125, place the decimal point on left of 0125 that is , 0.0125)

Decimal Fraction Practice Problems

Question 1: What decimal of an hour is a second?

1. .0025
2. .0256
3. .00027
4. .000126

Question 2: If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 =?

1. 172
2. 72
3. 2
4. 172

Question 3: When 0.232323….. is converted into a fraction, then the result is:

1. 1/5
2. 2/9
3. 23/99
4. 23/100

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Question 4: 3889 + 12.952 – ? = 3854.002

1. 095
2. 752
3. 932
4. 95

Question 5: If 144/ 0.144 = 14.4/ X, then the value of x is:

1. 0144
2. 44
3. 4
4. 144

Question 6: The rational number for recurring decimal 0.125125…. is:

1. 63/487
2. 119/993
3. 125/999
4. None of these

Question 7: Which of the following fractions is greater than 3/4 and less than 5/6?

1. 1/2
2. 2/3
3. 4/5
4. 9/10

Question 8: 617 + 6.017 + 0.617 + 6.0017 = ?

1. 2963
2. 965
3. 6357
4. None of these

Question 9: 0.002 x 0.5 =?

1. 0001
2. 001
3. 01
4. 1

Question 10: How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?

1. 5
2. 6
3. 7
4. None of these

Question 11: The correct expression of 6.46 in the fractional form is:

1. 646/99
2. 64640/1000
3. 640/100
4. 640/99

Question 12: The fraction 101 (27/100000) in decimal for is:

1. .01027
2. .10127
3. 00027
4. 000027

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Question 13: 4.036 divided by 0.04 gives :

1. 009
2. 09
3. 9
4. None of these

Question 14: Which of the following is equal to 3.14 x 106?

1. 314
2. 3140
3. 3140000
4. None of these

Question 15: The expression (11.98 x 11.98 + 11.98 x X + 0.02 x 0.02) will be a perfect square for x equal to:

1. 02
2. 2
3. 04
4. 4

Question 16: Product of 3. 0.03 × 0.0124 = ?

1. 72 × 10-6
2. 72 × 10-5
3. 72 × 10-3
4. 72 × 10-4

Question 17: When .36 is written in simplest fractions form, the sum of the numerator and the denominator is:

1. 15
2. 30
3. 45
4. 60

Question 18: 337.62+8.591+34.4 =?

1. 722
2. 622
3. 611
4. 94

Question 19: 34.95+240.016+23.98=?

1. 1057
2. 222
3. 946
4. 09

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Question 20: 48.95 – 32.006 =?

1. 091
2. 34
3. 97
4. 944

Question 21: 12.1212 + 17.0005 – 9.1102 =?

1. 0017
2. 0216
3. 0115
4. 1115

Question 22: 3889 + 12.952 –? = 3854.002

1. 015
2. 641
3. 943
4. 95

Question 23: Which of the following fractions is greater than 3/5 and less than 6/7?

1. 7/8
2. 1/3
3. 2/3
4. 1/2

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Question 24: Convert 0.343434….. into a fraction

1. 31/99
2. 32/99
3. 33/99
4. 34/99

Question 25: 926 + 9.026 + 0.926 + 9.0026 = ?

1. 9546
2. 1246
3. 4246
4. 9446