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fractions-and-decimals
Published in: Aptitude

Fractions and Decimals

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  • A fraction is an expression that indicates the quotient of two quantities.
  • A fraction has two parts, Numerator and Denominator. Numerator is the number at the top of the fraction and denominator is the number at the bottom of the fraction.

Converting a fraction to a decimal:

      1/4 = 1 ÷ 4.00 = 0.25

Converting a fraction to a percent:

  • Multiply the fraction by 100 and reduce it. Then, attach a percent sign.

         1/4 x 100/1 = 100/4 = 25/1 = 25%

 Converting a decimal to a fraction:

  • Starting from the decimal point, count the decimal places. If there is one decimal place, put the number over 10 and reduce. If there are two places, put the number over 100 and reduce. If there are three places, put it over 1000 and reduce, and so on.
  • The convertion would be 0.25 = 25/100 = 1/4

Converting a decimal to a percent:

  • Move the decimal point two places to the right. Then, attach a percent sign.
  • The convertion would be 0.25 = 25%

Converting a percent to a decimal:

  • Move the decimal point two places to the left. Then, drop the percent sign.
  • The convertion would be 25% = 0.25

Converting a percent to a fraction:

Divide the denominator (the bottom part) into the numerator (the top part):

  • Put the number over 100 and reduce. Then, drop the percent sign.
  • The convertion could be 25% = 25/100 = 1/4

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Fraction and decimals - Question and Answers

Congratulations - you have completed Fraction and decimals - Question and Answers. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1
Which of the following fractions is greater than 3/4 and less than 5/6?
A
1/2
B
2/3
C
4/5
D
9/10
Question 1 Explanation: 
3/4 = 0.75, 5/6 = 0.833, 1/2 = 0.5, 2/3 = 0.66, 4/5 = 0.8, 9/10 = 0.9
Clearly, 0.8 lies between 0.75 and 0.833
Therefore 4/5 lies between 3/4 and 5/6
Question 2
3.87 - 2.59 = ?
A
1.2
B
1.20
C
1.27
D
1.28
Question 2 Explanation: 
3.87 - 2.59 = (3 + 0.87) - (2 + 0.59)
= (3 + 87/99) - (2 + 59/99)
= 1+(87/99 – 59/99 )
= 1+(28/99) = 1.28
Question 3
4.036 divided by 0.04 gives?
A
1.009
B
10.09
C
100.9
D
None of these
Question 3 Explanation: 
(4.036 / 0.04) = (403.6 / 4) = 100.9
Question 4
(0.0203 x 2.92) / (0.0073 x 14.5 x 0.7) = ?
A
0.8
B
1.45
C
2.40
D
3.25
Question 4 Explanation: 
(0.0203 x 2.92) / (0.0073 x 14.5 x 0.7) = (203 x 292) / (73 x 145 x 7) = 4/5 = 0.8
Question 5
The fraction 101 27/100000 in decimal for is?
A
.01027
B
.10127
C
101.00027
D
101.000027
Question 5 Explanation: 
101 27/100000 = 101 + (27/100000) = 101 + .00027 = 101.00027
Question 6
The rational number for recurring decimal 0.125125.... is ?
A
63/487
B
119/993
C
125/999
D
None of these
Question 6 Explanation: 
0.125125... = 0.125 = 125/999
Question 7
617 + 6.017 + 0.617 + 6.0017 = ?
A
A. 6.2963
B
62.965
C
629.6357
D
None of these
Question 7 Explanation: 
617.00
6.017
0.617
+ 6.0017
--------
629.6357
---------
Question 8
The value of (489.1375 x 0.0483 x 1.956)/(0.0873 x 92.581 x 99.749) is closest to?  
A
0.006
B
0.06
C
0.6
D
6
Question 8 Explanation: 
(489.1375 x 0.0483 x 1.956)/(0.0873 x 92.581 x 99.749) = (489 x 0.05 x 2)/0.09 x 93 x 100
= 489/(9 x 93 x 10)
= 163/279 * 1/10
= 0.58/10
= 0.058 = 0.06
Question 9
0.002 x 0.5 = ?
A
0.0001
B
0.001
C
0.01
D
0.1
Question 9 Explanation: 
2 x 5 = 10
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Question 10
34.95 + 240.016 + 23.98 = ?
A
298.0946
B
298.111
C
A. 298.946
D
299.09
Question 10 Explanation: 
34.95
240.016
+ 23.98
--------
298.946
--------
Question 11
Which of the following is equal to 3.14 x 106 ?
A
314
B
3140
C
3140000
D
None of these
Question 11 Explanation: 
3.14 x 106 = 3.14 x 1000000 = 3140000
Question 12
The least among the following is?
A
0.2
B
1 ÷ 0.2
C
0.2
D
(0.2)2
Question 12 Explanation: 
1 ÷ 0.2 = 1/0.2 = = 10/2 = 5
0.2 = 0.222...
(0.2)2 = 0.04
0.04 < 0.2 < 0.22....<5
Since 0.04 is the least, so (0.2)2 is the least
Question 13
(5 x 1.6 - 2 x 1.4)/1.3 = ?
A
0.4
B
1.2
C
1.4
D
4
Question 13 Explanation: 
Given Expression = (8 - 2.8)/1.3 = 5.2/1.3 = 52/13 = 4
Question 14
How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?
A
5
B
6
C
7
D
None of these
Question 14 Explanation: 
Sum of decimal places = 7
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point
Question 15
0.04 x 0.0162 is equal to?
A
6.48 x 10-3
B
6.48 x 10-4
C
6.48 x 10-5
D
6.48 x 10-6
Question 15 Explanation: 
4 x 162 = 648, Sum of decimal places = 6
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10-4
Question 16
(4.2 x 4.2 - 1.9 x 1.9)/(2.3 x 6.1) is equal to?
A
0.5
B
1.0
C
20
D
22
Question 16 Explanation: 
Given Expression = [(a2 - b2)/(a + b)(a - b)] = (a2 - b2)/(a2 - b2) = 1
Question 17
If 144/(0.144) = (14.4)/x, then the value of x is?  
A
0.0144
B
1.44
C
14.4
D
144
Question 17 Explanation: 
144/0.144 = 14.4/x
144 * 1000/144 = 14.4 / x
x = 14.4 / 1000 =0.0144
Question 18
The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y?
A
2010
B
2011
C
2012
D
2013
Question 18 Explanation: 
Suppose commodity X will cost 40 paise more than Y after z years
Then, (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40
0.25z = 0.40 + 2.10
z = 2.50/0.25 = 250/25 = 10
X will cost 40 paise more than Y 10 years after 2001 i.e., 2011
Question 19
When 0.232323..... is converted into a fraction, then the result is?
A
1/5
B
2/9
C
23/99
D
23/100
Question 19 Explanation: 
0.232323... = 0.23 = 23/99
Question 20
.009/? = .01
A
.0009
B
.09
C
.9
D
9
Question 20 Explanation: 
Let .009/x = .01 Then x = .009/.01 = .9/1 =.9
Question 21
The expression (11.98 x 11.98 + 11.98 * x + 0.02 x 0.02) will be a perfect square for x equal to?
A
0.02
B
0.2
C
0.04
D
0.4
Question 21 Explanation: 
Given expression = (11.98)2 + (0.02)2 + 11.98 * x
For the given expression to be a perfect square, we must have
11.98 * x = 2 * 11.98 * 0.02 or x = 0.04
Question 22
[(0.1667)(0.8333)(0.3333)] / [(0.2222)(0.6667)(0.1250)]is approximately equal to?
A
2
B
2.40
C
2.43
D
2.50
Question 22 Explanation: 
Given expression = [(0.1667)(0.8333)(0.3333)] / [(0.2222)(0.6667)(0.1250)]
= 3333/2222 x [(1/6 x 5/6)] / [(2/3 x 125/1000)]
= (3/2 x 1/6 x 5/6 x 3/2 x 8)
= 5/2 = 2.50
Question 23
3889 + 12.952 - ? = 3854.002
A
47.095
B
47.752
C
47.932
D
47.95
Question 23 Explanation: 
Let 3889 + 12.952 - x = 3854.002
Then x = (3889 + 12.952) - 3854.002
=> 3901.952 - 3854.002
=> 47.95
Question 24
Evaluate (2.39)2 – (1.61)2/ (2.39 – 1.61)?
A
2
B
4
C
6
D
8
Question 24 Explanation: 
Given Expression = a2-b2 /a–b = (a+b)(a-b)/(a-b)
=> (a+b) = (2.39 + 1.61) = 4
Question 25
What decimal of an hour is a second?
A
.0025
B
.0256
C
.00027
D
.000126
Question 25 Explanation: 
Required decimal = 1/(60 x 60) = 1/3600 = .00027
Question 26
The value of [(0.96)3- (0.1)3] / [(0.96)2 + 0.096 + (0.1)2] is?
A
0.86
B
0.95
C
0.97
D
1.06
Question 26 Explanation: 
Given expression = [(0.96)3- (0.1)3] / [(0.96)2 +(0.96 x 0.1) +(0.1)2
=> [(a3 - b3) / (a2 + ab + b2)] = (a - b)
=> (0.96 – 0.1) = 0.86
Question 27
The value of (0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02) / (0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04) is?
A
0.0125
B
0.125
C
0.25
D
0.5
Question 27 Explanation: 
Given expression = (0.1)3 + (0.02)3 / 23[(0.1)3+(0.02)3] = 1/8 = 0.125
Question 28
If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 =?
A
0.172
B
1.72
C
17.2
D
172
Question 28 Explanation: 
29.94/1.45 = 299.4/14.5
= (2994/14.5) x (1/10) [ Here, Substitute 172 in the place of 2994/14.5]
=> 172/10
=> 17.2
Question 29
If 2A = 3B and 4B = 5C, then A:C is?
A
4:3
B
8:15
C
15:8
D
3:4
Question 29 Explanation: 
A/B = 3/2 And B/C = 5/4
A/C = A/B * B/C = 3/2 * 5/4 = 15/8
Question 30
How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
A
5
B
6
C
7
D
None of these
Question 30 Explanation: 
Sum of decimal places = 7
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point
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