Explanation / Important formulas:
- 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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Fractions and Decimals - Test
Fraction and decimals - Question and Answers
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Question 1
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Which of the following fractions is greater than 3/4 and less than 5/6?
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1/2
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2/3
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4/5
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9/10
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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
Clearly, 0.8 lies between 0.75 and 0.833
Therefore 4/5 lies between 3/4 and 5/6
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Question 2
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3.87 - 2.59 = ?
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1.2
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1.20
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1.27
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1.28
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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
= (3 + 87/99) - (2 + 59/99)
= 1+(87/99 – 59/99 )
= 1+(28/99) = 1.28
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Question 3
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4.036 divided by 0.04 gives?
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1.009
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10.09
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100.9
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None of these
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Question 3 Explanation:
(4.036 / 0.04) = (403.6 / 4) = 100.9
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Question 4
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(0.0203 x 2.92) / (0.0073 x 14.5 x 0.7) = ?
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0.8
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1.45
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2.40
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3.25
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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
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Question 5
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The fraction 101 27/100000 in decimal for is?
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.01027
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.10127
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101.00027
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101.000027
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Question 5 Explanation:
101 27/100000 = 101 + (27/100000) = 101 + .00027 = 101.00027
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Question 6
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The rational number for recurring decimal 0.125125.... is ?
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63/487
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119/993
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125/999
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None of these
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Question 6 Explanation:
0.125125... = 0.125 = 125/999
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Question 7
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617 + 6.017 + 0.617 + 6.0017 = ?
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A.
6.2963 |
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62.965
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629.6357
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None of these
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Question 7 Explanation:
617.00
6.017
0.617
+ 6.0017
--------
629.6357
---------
6.017
0.617
+ 6.0017
--------
629.6357
---------
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Question 8
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The value of (489.1375 x 0.0483 x 1.956)/(0.0873 x 92.581 x 99.749) is closest to?
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0.006
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0.06
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0.6
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6
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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
= 489/(9 x 93 x 10)
= 163/279 * 1/10
= 0.58/10
= 0.058 = 0.06
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Question 9
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0.002 x 0.5 = ?
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0.0001
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0.001
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0.01
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0.1
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Question 9 Explanation:
2 x 5 = 10
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Sum of decimal places = 4
0.002 x 0.5 = 0.001
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Question 10
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34.95 + 240.016 + 23.98 = ?
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298.0946
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298.111
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A.
298.946 |
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299.09
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Question 10 Explanation:
34.95
240.016
+ 23.98
--------
298.946
--------
240.016
+ 23.98
--------
298.946
--------
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Question 11
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Which of the following is equal to 3.14 x 106 ?
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314
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3140
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3140000
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None of these
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Question 11 Explanation:
3.14 x 106 = 3.14 x 1000000 = 3140000
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Question 12
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The least among the following is?
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0.2
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1 ÷ 0.2
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0.2
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(0.2)2
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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
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
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Question 13
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(5 x 1.6 - 2 x 1.4)/1.3 = ?
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0.4
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1.2
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1.4
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4
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Question 13 Explanation:
Given Expression = (8 - 2.8)/1.3 = 5.2/1.3 = 52/13 = 4
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Question 14
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How many digits will be there to the right of the decimal point in the product of 95.75 and .02554?
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5
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6
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7
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None of these
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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
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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Question 15
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0.04 x 0.0162 is equal to?
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6.48 x 10-3
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6.48 x 10-4
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6.48 x 10-5
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6.48 x 10-6
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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
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10-4
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Question 16
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(4.2 x 4.2 - 1.9 x 1.9)/(2.3 x 6.1) is equal to?
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0.5
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1.0
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20
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22
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Question 16 Explanation:
Given Expression = [(a2 - b2)/(a + b)(a - b)] = (a2 - b2)/(a2 - b2) = 1
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Question 17
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If 144/(0.144) = (14.4)/x, then the value of x is?
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0.0144
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1.44
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14.4
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144
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Question 17 Explanation:
144/0.144 = 14.4/x
144 * 1000/144 = 14.4 / x
x = 14.4 / 1000 =0.0144
144 * 1000/144 = 14.4 / x
x = 14.4 / 1000 =0.0144
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Question 18
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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?
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2010
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2011
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2012
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2013
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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
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
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Question 19
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When 0.232323..... is converted into a fraction, then the result is?
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1/5
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2/9
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23/99
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23/100
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Question 19 Explanation:
0.232323... = 0.23 = 23/99
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Question 20
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.009/? = .01
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.0009
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.09
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.9
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9
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Question 20 Explanation:
Let .009/x = .01 Then x = .009/.01 = .9/1 =.9
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Question 21
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The expression (11.98 x 11.98 + 11.98 * x + 0.02 x 0.02) will be a perfect square for x equal to?
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0.02
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0.2
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0.04
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0.4
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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
For the given expression to be a perfect square, we must have
11.98 * x = 2 * 11.98 * 0.02 or x = 0.04
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Question 22
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[(0.1667)(0.8333)(0.3333)] / [(0.2222)(0.6667)(0.1250)]is approximately equal to?
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2
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2.40
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2.43
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2.50
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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
= 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
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Question 23
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3889 + 12.952 - ? = 3854.002
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47.095
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47.752
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47.932
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47.95
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Question 23 Explanation:
Let 3889 + 12.952 - x = 3854.002
Then x = (3889 + 12.952) - 3854.002
=> 3901.952 - 3854.002
=> 47.95
Then x = (3889 + 12.952) - 3854.002
=> 3901.952 - 3854.002
=> 47.95
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Question 24
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Evaluate (2.39)2 – (1.61)2/ (2.39 – 1.61)?
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2
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4
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6
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8
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Question 24 Explanation:
Given Expression = a2-b2 /a–b = (a+b)(a-b)/(a-b)
=> (a+b) = (2.39 + 1.61) = 4
=> (a+b) = (2.39 + 1.61) = 4
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Question 25
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What decimal of an hour is a second?
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.0025
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.0256
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.00027
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.000126
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Question 25 Explanation:
Required decimal = 1/(60 x 60) = 1/3600 = .00027
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Question 26
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The value of [(0.96)3- (0.1)3] / [(0.96)2 + 0.096 + (0.1)2] is?
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0.86
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0.95
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0.97
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1.06
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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
=> [(a3 - b3) / (a2 + ab + b2)] = (a - b)
=> (0.96 – 0.1) = 0.86
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Question 27
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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?
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0.0125
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0.125
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0.25
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0.5
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Question 27 Explanation:
Given expression = (0.1)3 + (0.02)3 / 23[(0.1)3+(0.02)3] = 1/8 = 0.125
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Question 28
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If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 =?
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0.172
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1.72
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17.2
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172
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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
= (2994/14.5) x (1/10) [ Here, Substitute 172 in the place of 2994/14.5]
=> 172/10
=> 17.2
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Question 29
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If 2A = 3B and 4B = 5C, then A:C is?
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4:3
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8:15
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15:8
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3:4
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Question 29 Explanation:
A/B = 3/2 And B/C = 5/4
A/C = A/B * B/C = 3/2 * 5/4 = 15/8
A/C = A/B * B/C = 3/2 * 5/4 = 15/8
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Question 30
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How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ?
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5
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6
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7
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None of these
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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
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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