Decimal Fractions  Important Formulas and Examples
Decimal Fraction Formulas
Decimal Fractions: Fractions in which denominators are powers of 10 are known as decimal fractions.
1/10 = 1 tenth = .1
1/100 = 1 hundredth = .01
9/100 = 99 hundredth = .99
7/1000 = 7 thousandths =.007
Conversion of a 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 = 1/4
2.008 = 2008/1000 = 251/125.
Annexing zeros to the extreme right of a decimal fraction does not change its value.
0.8 = 0.80 = 0.800, etc.
If numerator and denominator of a fraction contain the same number of decimal places, then we remove the decimal sign.
1.84/2.99 = 184/299 = 8/13
0.365/0.584 = 365/584 = 5
Operations on Decimal Fractions :
1) Addition and Subtraction of Decimal Fractions : The given numbers are so placed under each other that the decimal points lie in one column. The numbers so arranged can now be added or subtracted in the usual way.
2) Multiplication of a Decimal Fraction By a Power of 10 : Shift the 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 = 0.0730 x 10000 = 730.
Multiplication of Decimal Fractions : Multiply the given numbers considering them without the decimal point. Now, in the product, the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal places in the given numbers. Suppose we have to find the product (.2 x .02 x .002).
Now, 2x2x2 = 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
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. Suppose, we have to arrange the fractions 3/5, 6/7 and 7/9 in descending order.
now,
3/5 = 0.6
6/7 = 0.857
7/9 = 0.777....
since 0.857 > 0.777...> 0.6
so 6/7>7/9>3/5
Recurring Decimal : If in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal. In a recurring decimal, if a single figure is repeated, then it is expressed by putting a dot on it. If a set of figures is repeated, it is expressed by putting a bar on the set, Thus
1/3 = 0.3333….= 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.
Converting a Pure Recurring Decimal Into Vulgar Fraction : Write the repeated figures only once in the numerator and take as many nines in the denominator as is the number of repeating figures. thus ,
0.5 = 5/9; 0.53 = 53/59 ;0.067 = 67/999; etc...
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. e.g., 0.17333= 0.173.
Converting a Mixed Recurring Decimal Into Vulgar Fraction : In the numerator, take the difference between the number formed by all the digits after decimal point (taking repeated digits only once) and that formed by the digits which are not repeated, In the denominator, take the number formed by as many nines as there are repeating digits followed by as many zeros as is the number of nonrepeating digits. Thus
0.16 = (161) / 90 = 15/19 = 1/6;
Decimal Fraction Solved Examples
Example 1: Convert (i) 0.75 and (ii) 2.008 into vulgar fractions.
Solutions:
i)
ii)
Rule  for Converting a decimal into a vulgar fractions: In the denominator put 1 under decimal point and annex with it as many zeros as the number of digits after the decimal point. Next , remove the decimal point and write whole number in numerator. Reduce it to lowest form.
Remark  Annexing zeros to the extreme right of a decimal fraction does not change its value.
Addition and subtraction of decimal fractions.
Example 2: Convert (i) 45.7 + 3.098 + 0.79 + 0.8 = ?
(ii) 9.053 – 3.69 = ?
Solution:
i) 45.7 
ii) 9.053 
+ 3.098   3.69 
+0.79  5.363 
+0.8  
50.388 
Thus for addition the given numbers are so placed under each other that the decimal point lie in column. Now, the number can be added or subtracted as usual putting the decimal point under the decimal points.
Example 3: Evaluate i) 6.4209100 ii) 0.037910
Solution:
1 ) 6.4209100 = 642.09
2) 0.0379100 = 0.379
3) 0.0091000 = 9
Thus when we multiply 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 4: Find the productions
1) 2.2572.1
2) 2.79 1.31
3) 50.50.0005
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, result is 36549. Total decimal places are 4, put decimal counting four digits from right.
(3) 5 0.50.050.0005 = 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.
Example 5: Evaluate (1) 0.72 + 9, (2) 0.0625 + 5, (3) 0.000121 + 11
Solution:
1) 0.72 + 9 ==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) =0.0125
(Divided 625 by 5, get 125, place the decimal point on left of 0125 that is , 0.0125)
3) 0.000121 + 11= = 0.000011
(Divided 121 bt 11, get 11 as result, place decimal on left of 1.00011 that is, 0.000011.)
Division of a decimal fraction by a decimal fraction.
Example 6: Evaluate (1) 0.26 + 0.06 (2) 0.0077 + 0.11
Solution:
1)
2) 0.0077 + 0.11 =
= 0.07
Decimal Fractions  Questions from Previous Year Papers
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Question 1 of 14
1. Question
1 pointsFind the products 6.3204 × 100
Correct
6.3204 × 100 = = 632.04
Incorrect
6.3204 × 100 = = 632.04

Question 2 of 14
2. Question
1 pointsWhat value will come in place of question mark in the following equation?
Correct
= 0.6
x = = = 0.01
Incorrect
= 0.6
x = = = 0.01

Question 3 of 14
3. Question
1 pointsWhat decimal of an hour is a second ?
Correct
Required decimal = = 0.00027
Incorrect
Required decimal = = 0.00027

Question 4 of 14
4. Question
1 pointsThe value of is(SBI 1995)
Correct
Given expression = = 0.125
Incorrect
Given expression = = 0.125

Question 5 of 14
5. Question
1 pointsWhen 0.232323... is converted into a fraction, then the result (SBI 2000)
Correct
0.232323.... =
Incorrect
0.232323.... =

Question 6 of 14
6. Question
1 pointsThe expression (11.98 11.98 + 11.98 x + 0.02 0.02) will be a perfect square for x equal to
(SBI PO 2002)Correct
Given expression =
For the given expression to be a perfect square, we must have
11.98 x = 2 11.98 0.02
x = 0.04
Incorrect
Given expression =
For the given expression to be a perfect square, we must have
11.98 x = 2 11.98 0.02
x = 0.04

Question 7 of 14
7. Question
1 points0.04 0.0162 is equal to:
Correct
4 162 = 648 Sum of decimal places = 6
0.04 0.0162 = 0.000648 =
Incorrect
4 162 = 648 Sum of decimal places = 6
0.04 0.0162 = 0.000648 =

Question 8 of 14
8. Question
1 pointsHow many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
Correct
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 4 = 20), so there will be 6 significant digits to the right of the decimal point.Incorrect
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 4 = 20), so there will be 6 significant digits to the right of the decimal point. 
Question 9 of 14
9. Question
1 points4.036 divided by 0.04 gives
Correct
= 100.9
Incorrect
= 100.9

Question 10 of 14
10. Question
1 pointsGiven that 268 74 = 19832, Find the value of 2.68 0.74.
Correct
Sum of decimal places = (2 + 2) = 4.
So, 2.68 0.74 = 1.9832.
Incorrect
Sum of decimal places = (2 + 2) = 4.
So, 2.68 0.74 = 1.9832.

Question 11 of 14
11. Question
1 points= 0.2689 then find the value of
Correct
=> 10000 × 0.2689 = 2689
Incorrect
=> 10000 × 0.2689 = 2689

Question 12 of 14
12. Question
1 pointsWhat value will replace the question mark in the following equations?
5172.49 + 378.352 + ? = 9318.678
Correct
Let 5172.49 + 378.352 + x = 9318.678.
Then, x = 9318.678 – (5172.49 + 378.352)
=> 9318.678 – 550.842
=> 3767.836.
Incorrect
Let 5172.49 + 378.352 + x = 9318.678.
Then, x = 9318.678 – (5172.49 + 378.352)
=> 9318.678 – 550.842
=> 3767.836.

Question 13 of 14
13. Question
1 pointsIf 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?
Correct
=
=
= = 17.2
Incorrect
=
=
= = 17.2

Question 14 of 14
14. Question
1 points3889 + 12.952  ? = 3854.002
Correct
Let 3889 + 12.952  x = 3854.002.
Then x = (3889 + 12.952)  3854.002
= 3901.952  3854.002
= 47.95.
Incorrect
Let 3889 + 12.952  x = 3854.002.
Then x = (3889 + 12.952)  3854.002
= 3901.952  3854.002
= 47.95.
Decimal Fractions  Questions from Previous Year Papers