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Converting between fractions or decimals and percentages - class-VIII

Description: converting between fractions or decimals and percentages
Number of Questions: 44
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Tags: comparison of quantities percentage maths percent and percentage percent comparing quantities using proportion comparing quantity comparing quantities
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Convert the following percents into fractions:

$33\dfrac{1}{3}\%$

  1. $\dfrac{99}{100}$

  2. $\dfrac{3}{100}$

  3. $\dfrac{33}{100}$

  4. $\dfrac{1}{3}$


Correct Option: D
Explanation:

Given percent  $={33}\dfrac{1}{3}\%$

Now, ${33}\dfrac{1}{3}=\dfrac{(33\times3)+1}{3}=\dfrac{100}{3}$
${33}\dfrac{1}{3}\%=\dfrac {100}{3}\times\dfrac{1}{100}=\dfrac {1} {3}$

Convert the following percents into fractions:

$6\dfrac{1}{4}\%$

  1. $\dfrac{2}{16}$

  2. $\dfrac{1}{16}$

  3. $\dfrac{25}{4}$

  4. $\dfrac{1}{4}$


Correct Option: B
Explanation:
Given percent $={6}\dfrac{1}{4}\%$
Now, ${6}\dfrac{1}{4}=\dfrac{(6\times4)+1}{4}$
                 $=\dfrac{25}{4}$
$\implies{6}\dfrac{1}{4}\%=\dfrac {25}{4}\times\dfrac{1}{100}$
                      $=\dfrac {1} {16}$

Convert the following percents into fractions:

$12\%$

  1. $\dfrac{1}{25}$

  2. $\dfrac{2}{25}$

  3. $\dfrac{3}{25}$

  4. $\dfrac{4}{25}$


Correct Option: C
Explanation:

$12\%=\dfrac{12}{100}=\dfrac{3}{25}$

$16\frac{2}{3}\% $ of $600$gm $ - 33\frac{1}{3}\% $ of $180$gm

  1. $20$ gm

  2. $30$ gm

  3. $40$ gm

  4. $60$ gm


Correct Option: C
Explanation:
$16 \dfrac{2}{3}\%$ of $600\ gm-33 \dfrac{1}{3} \%$ of $180\ gm$
$\Rightarrow \left[ \dfrac{50}{3} \times \dfrac{1}{100} (600)- \left( \dfrac{100}{3} \times \dfrac{1}{100} \right) (180) \right] gm$
$\Rightarrow \left[ \dfrac{600}{6}- \dfrac{180}{3} \right]\ gm$
$\Rightarrow (100-60)\ gm$
$\Rightarrow 40\ gm$
$\therefore [16 2/3 \% \ of\ 600\ gm-33 1/3 \% \ of\ 180\ gm]=40\ gm$

$138\%$ is equal to:

  1. $\displaystyle \frac{68}{50}$

  2. $\displaystyle \frac{69}{50}$

  3. $13.8$

  4. $1.83$


Correct Option: B
Explanation:

Given, $138 \%=.....$

We can write it as,
$138 \%  =\displaystyle \frac{138}{100} = \frac{69}{50}$ .... On dividing by $2$

$128\%$ is equal to:

  1. $\displaystyle \frac{32}{25}$

  2. $\displaystyle \frac{68}{50}$

  3. $12.8$

  4. $0.128$


Correct Option: A
Explanation:

Given, we need to find $ 128 \%$

$\therefore 128$ $\%=$ $\displaystyle \frac{128}{100}=\frac{32}{25}$
Hence, option A is correct.

1.8% $=$ .......

  1. 1.800

  2. 1.8

  3. 0.18

  4. 0.018


Correct Option: D
Explanation:

$1.8% $= $\dfrac{1.8}{100} = 0.018$

In a class of $200, 75\%$ were present How many were absent?

  1. $150$

  2. $50$

  3. $75$

  4. $125$


Correct Option: B
Explanation:

Number of absent members
= 25 % of 200
= $\displaystyle \frac{25}{100}\times 200=50$

80% of a non-leap year $= ....... $days

  1. $288$

  2. $256$

  3. $292$

  4. $270$


Correct Option: C
Explanation:

A non-leap year has $= 365$ days

$80\%$ of a non-leap year $= \dfrac{80}{100}\times 365$
                                        $= 292$ days

The percentage equivalent to $\displaystyle\frac{3}{8}$ is 

  1. $37.5\%$

  2. $0.375\%$

  3. $40\%$

  4. $3.75\%$


Correct Option: A
Explanation:
We need to find percentage equivalent to $\dfrac {3}{8}$.
We know gain $% =$ $\displaystyle\frac{3}{8}\,=\, \frac{3}{8}\,\times\,\frac{100}{100}\,$
$=\, \dfrac{37.5}{100}\,$
$=\, 37.5 %$

0.9 percent can be expressed as

  1. $0.009$

  2. $0.09$

  3. $0.0009$

  4. $0.9$


Correct Option: A
Explanation:

0.9% = $\displaystyle\frac{0.9}{100}\,=\, 0.009$

A person spends $33\frac{1}{3}$% of his total income on food.Amount spend on food will be what part of his income

  1. $33\frac{1}{3}$

  2. $3\frac{1}{33}$

  3. $\frac{1}{3}$

  4. $\frac{1}{33}$


Correct Option: C
Explanation:

Let the persons income = $I$
He spends, $33 \frac{1}{3}$ % of his income = $\frac{100}{3}$ %
Thus, Money spend on food = $\frac{100}{3}$ % of I = $\frac{\frac{100}{3}}{100}$ of I = $\frac{I}{3}$

Thus, the man spends $\frac{1}{3}$ of his income on food.

$\frac{1}{8}$% means 

  1. $\frac{1}{8}$

  2. $\frac{100}{8}$

  3. $\frac{8}{100}$

  4. $\frac{1}{800}$


Correct Option: D
Explanation:

$\frac{1}{8}$ % = $\frac{\frac{1}{8}}{100} = \frac{1}{800}$

Express:


35% as fraction

  1. $\displaystyle\frac{7}{20}$

  2. $\displaystyle\frac{7}{30}$

  3. $\displaystyle\frac{14}{30}$

  4. $\displaystyle\frac{7}{10}$


Correct Option: A
Explanation:

$35$ % = $\frac{35}{100}$ = $\frac{7}{20}$

Express $18\%$ as ratio

  1. $9:50$

  2. $9:100$

  3. $9:25$

  4. $9:75$


Correct Option: A
Explanation:

$18$ % = $\dfrac{18}{100}$ = $\dfrac{9}{50}$

Square root of 49% is?

  1. $0.7$

  2. $70$%

  3. $7$

  4. $0.07$


Correct Option: A
Explanation:

$49$% can be written as $\dfrac {49}{100}$


Therefore, 

$\sqrt {\dfrac {49}{100} }= \dfrac{7}{10} = 0.7$

Express the following as fraction and simplify:

$420 \%$

  1. $\cfrac {41}{5}$

  2. $\cfrac {1}{5}$

  3. $\cfrac {4}{5}$

  4. $\cfrac {21}{5}$


Correct Option: D
Explanation:

To convert a percent to a fraction, write it over a denominator of 100 and simplify:
$420\% = \cfrac{420}{100} = \cfrac{21}{5}$

What will be the fraction of $20\%$ ?

  1. $\dfrac{1}{4}$

  2. $\dfrac{1}{5}$

  3. $\dfrac{1}{10}$

  4. $\dfrac{1}{20}$


Correct Option: B
Explanation:

The fraction of $20\%$ is 

$20\times \dfrac {1}{100}=\dfrac {1}{5}$
Hence, option B is correct.

$84\% =$ ______ in vulgar fraction.

  1. $\dfrac{11}{20}$

  2. $\dfrac{21}{25}$

  3. $\dfrac{31}{20}$

  4. $\dfrac{41}{20}$


Correct Option: B
Explanation:

Converting Given percent into simple fraction as :
$84\% =$ $\dfrac{84}{100}$
Reduce the fraction, we get
$\dfrac{84}{100}=\dfrac{21}{25}$

Convert $75\%$ into vulgar fraction.

  1. $\dfrac{1}{4}$

  2. $\dfrac{2}{4}$

  3. $\dfrac{3}{4}$

  4. $\dfrac{5}{4}$


Correct Option: C
Explanation:

Converting a given fraction into simple fraction as:

$75\% =$ $\dfrac{75}{100}$
Reduce the fraction, we get
$\dfrac{75}{100}=\dfrac{3}{4}$

What is $45\%$ in decimal?

  1. $0.45$

  2. $0.0045$

  3. $45.00$

  4. $0.54$


Correct Option: A
Explanation:
Converting a given fraction into decimal as:

$45\% =$ $\dfrac{45}{100}$

On dividing, we get
$\dfrac{45}{100} = 0.45$

$60\%$ of what number if $45$?

  1. $27$

  2. $30$

  3. $60$

  4. $75$

  5. $90$


Correct Option: D
Explanation:

Let the number be $ x $
So, $ 60 $ $\%$ of $ x = 45 $
$ \Rightarrow  \dfrac {60}{100} \times x = 45 $

$\Rightarrow 60 \times x=45 \times 100$
$ \Rightarrow  x =75 $

$38$ liters of milk was poured into a tub and the tub was found to be $5\%$ empty. To completely fill the tub, what amount of additional milk must be poured?

  1. $1$ litres

  2. $2$ litres

  3. $3$ litres

  4. $4$ litres


Correct Option: B
Explanation:

After pouring $38$ litres of milk, $5\%$ is found empty.
Here $95\%$ of capacity of the tub $= 38$ liters
Therefore, capacity of the tub $= 30\times \dfrac {100}{95} $ litres $= 40$ litres
Thus additional milk to be poured $= (40 - 38) $ i.e., $2$ litres.

$1\%$ of $1\%$ of $25\%$ of $1000$ is :

  1. $0.25$

  2. $0.025$

  3. $0.00025$

  4. $25$


Correct Option: B
Explanation:

We need to find value of $1\%\,\text{of}\,1\%\,\text{of}\,25\%\,\text{of}\,1000$

This would be equal to $\dfrac{1}{100}\times \dfrac{1}{100}\times \dfrac{25}{100}\times 1000$
$=\dfrac{25}{1000}$
$=0.025$.

If $x\%$ of $24=64$, then the value of x is __________.

  1. $\displaystyle 37\frac{1}{2}$

  2. $\displaystyle 133\frac{1}{3}$

  3. $\displaystyle 266\frac{2}{3}$

  4. $\displaystyle 66\frac{2}{3}$


Correct Option: C
Explanation:

$24\times\dfrac{x}{100}=64$

$x=\dfrac{64\times 100}{24}$$=266.667$$=266\dfrac{1}{3}$
Hence the correct answer is option C.

Choose the correct answer from the alternatives given :
A spider climbed $62\frac{1}{2}%$ of the height of the pole in one hour and in the next hour it covered $12\frac{1}{2}%$ of the remaining height. If poles height is 192 m. then distance climbed in second hour is

  1. $3$ m

  2. $5$ m

  3. $7$ m

  4. $9$ m


Correct Option: D
Explanation:

Remaining height = $\left (192 - \dfrac{125}{2}\% of 192 \right ) = $192- 120$ = 72 m$
Required distance (distance covered in second hour) then,
$\dfrac{25}{2}\% of\ 72 $= $\dfrac{25 \times 72}{2 \times 100} = 9 m$

Choose the correct answer from the alternatives given.
Prabhu purchased 30 kg of rice at the rate of Rs. 17.50 per kg and another 30 kg rice at a certain rate. He mixed the variety of two rice and sold the entire quantity at the rate of Rs.18 per kg and made 20% overall profit. At what price per kg did he purchase the lot of another 30 kg rice?

  1. Rs. 14.50

  2. Rs. 12.50

  3. Rs. 15.50

  4. Rs. 13.50


Correct Option: B
Explanation:

Let the price at which the other $30$ kg was bought be Rs. x.
CP of mixture = $\frac{100}{120}\times 18 = 15$
$\frac{2.5}{15 x} = \frac{30}{30}$
$15x=2.5$
Hence, x= Rs. $12.5$

Convert the following percents into fractions:

$\dfrac{1}{2}\%$

  1. $\dfrac{1}{100}$

  2. $\dfrac{2}{100}$

  3. $\dfrac{1}{200}$

  4. $\dfrac{3}{200}$


Correct Option: C
Explanation:

$a\%=\dfrac { a }{ 100 } $ in fraction

$\therefore \dfrac { 1 }{ 2 } \%=\dfrac { 1 }{ 2 } \times \dfrac { 1 }{ 100 } =\dfrac { 1 }{ 200 } $

Convert the following percents into fractions:

$40\dfrac{2}{3}\%$

  1. $\dfrac{61}{50}$

  2. $\dfrac{61}{100}$

  3. $\dfrac{61}{150}$

  4. $\dfrac{183}{150}$


Correct Option: C
Explanation:

$a\%=\dfrac { a }{ 100 } $ in fraction

$40\dfrac { 2 }{ 3 } \%=\dfrac { 122 }{ 3 } \%\ \quad \quad \quad =\dfrac { 122 }{ 3 } \times \dfrac { 1 }{ 100 } \ \quad \quad \quad  =\dfrac { 61 }{ 150 } $

15% of 10% of 20% of 1000 is 

  1. $1.50$

  2. $67$

  3. $150$

  4. $3$


Correct Option: D
Explanation:

$15\%$ of $10\%$ of $20\%$ of $1000$


$\Rightarrow 15\%$ of $10\%\left[\dfrac{20}{100}\times 1000\right]$

$\Rightarrow 15\%$ of $10\%$ of $200$

$\Rightarrow 15\%\left[\dfrac{10}{100}\times 200\right]$

$\Rightarrow 15\%$ of $20$

$\Rightarrow \dfrac{15}{100}\times 20$

$\Rightarrow  3$

$\therefore\ 15\%$ of $10\%$ of $20\%$ of $1000=3$

If $40$%of a number is equal to two-third of another number, what is the ratio of first number to the second numbers?

  1. 2:5

  2. 3:7

  3. 5:3

  4. 7:3


Correct Option: C
Explanation:
$(l-m) (lm+l+x^{2})=0$
 Let the number be $x _{1} y$
Given :- $40\% $ of $(x) = \dfrac{2}{3}$ of $(y)$
to find :-$\dfrac{x}{y}= ?$
$\dfrac{40}{100} \times x = \dfrac{2}{3} \times y$
$\dfrac{x}{y}= \dfrac{2}{3} \times \dfrac{100}{40}$
$\Rightarrow \dfrac{x}{y}= \dfrac{5}{3}$

$5\%$ of $600$

  1. $30$

  2. $60$

  3. $160$

  4. $600$


Correct Option: A
Explanation:

$5\%$ of $600=\dfrac{5}{100}\times 600=5\times 6=30$

Hence, the answer is $30.$

The possible percentage error in computing the parallel resistance $R$ of three resistances $R _{1},R _{2},R _{3}$ from the formula $\dfrac {1}{R}=\dfrac {1}{R _{1}}+\dfrac {1}{R _{2}}+\dfrac {1}{R _{3}}$, if $R _{1},R _{2},R _{3}$ are each by $1.2\%$

  1. $1.2$

  2. $1.3$

  3. $1.3$

  4. $1.7$


Correct Option: A

If $33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$, then $A\colon\,B\colon\,C$ is

  1. $\;24\colon2\colon9$

  2. $\;2\colon9\colon24$

  3. $\;9\colon2\colon24$

  4. $\;9\colon24\colon2$


Correct Option: C
Explanation:

$\;\displaystyle\frac{100}{3\times100}\times\,A=\displaystyle\frac{3}{2}\times\,B=\displaystyle\frac{1}{8}\times\,C=x\,(say)$
$\;\;\;\;\;\Rightarrow\;A=3x,\,B=\displaystyle\frac{2}{3}x,\,C=8x$
$\;\;\;\;\;\;\Rightarrow\;A\colon\,B\colon\,C=3\colon\displaystyle\frac{2}{3}\colon8=9\colon2\colon24$.

If the numerator of a fraction is increased by $300\%$ and the denominator is increased by $500\%$, the resultant fraction is $\displaystyle\frac{5}{12}$. What was the original fraction?

  1. $\;\displaystyle\frac{8}{5}$

  2. $\;\displaystyle\frac{5}{8}$

  3. $\;\displaystyle\frac{12}{5}$

  4. $\;\displaystyle\frac{5}{7}$


Correct Option: B
Explanation:

Let the original fraction be $\dfrac {p}{q}$. 

Then, $\displaystyle\frac{p+\displaystyle\frac{300}{100}P}{q+\displaystyle\frac{500}{100}P}=\displaystyle\frac{5}{12}$
$\Rightarrow \displaystyle\frac{4p}{6q}=\displaystyle\frac{5}{12}$
$\Rightarrow\;\displaystyle\frac{p}{q}=\displaystyle\frac{5}{12}\times\displaystyle\frac{6}{4}=\displaystyle\frac{5}{8}$

Half of $1$ percent written as a decimal is

  1. $0.2$

  2. $0.02$

  3. $0.05$

  4. $0.005$


Correct Option: D
Explanation:

Half of $ 1\%$ in decimals

It will be $\displaystyle \frac {1}{2} \times 1 \% = \displaystyle \frac {1}{2}\times  \frac {1}{100}$
$ = \displaystyle \frac {1}{200}= 0.005$

What percentage is equivalent to $\dfrac {3}{8}$ ?

  1. $33.33\%$

  2. $39\%$

  3. $37.5\%$

  4. $40\%$


Correct Option: C
Explanation:
$\dfrac {3}{8}$ can be written in percentage form as:
Equivalent percentage  $= \dfrac {(3 \times 100)}{8} = 37.5\%$
So, option C is correct.

If $m > 0$ and $x$ is $m$ percent of $y$, then in terms of $m$, $y$ is what percent of $x$ ? 

  1. $100$ m

  2. $\dfrac{1}{100}$ m

  3. $1$ m

  4. $10$ m

  5. $\dfrac {10000}{m}$


Correct Option: E
Explanation:

Given that : x is $m\%$ of y

$\Rightarrow x = \cfrac{m}{100} \times y$ 
Now, let's say that y is $k\%$ of x, then
$y = \dfrac{k}{100} \times x$
But $x= \cfrac{m}{100} \times y$
$\therefore y =\cfrac{k}{100} \times \cfrac{m}{100} \times y$
$k = \cfrac{10000}{m}$

Express $0.08\%$ as a fraction

  1. $\dfrac{1}{250}$

  2. $\dfrac{1}{1250}$

  3. $\dfrac{1}{125}$

  4. $\dfrac{1}{25}$


Correct Option: B
Explanation:

$0.08\%$ can be written as $\dfrac{0.08}{100}$

$=\dfrac{8}{10000}$
$=\dfrac{1}{1250}$
Hence, option B is correct.

Express the following as fraction and simplify:

$8 \%$

  1. $0$

  2. $\cfrac {1}{25}$

  3. $\cfrac {2}{25}$

  4. $\cfrac {4}{25}$


Correct Option: C
Explanation:

To convert a percent to a fraction, write it over a denominator of 100 and simplify:
$8\% = \cfrac{8}{100} = \cfrac{2}{25}$

Convert $75$% to a fraction

  1. $2/3$

  2. $3/4$

  3. $4/5$

  4. None


Correct Option: B
Explanation:

$75$%$=\cfrac{75}{100}=\cfrac{3}{4}$

Square root of $64$% is?

  1. $0.8$

  2. $0.72$

  3. $0.74$

  4. $0.76$


Correct Option: A
Explanation:

We have, $\sqrt{64\%}$


$\Rightarrow$  $\sqrt{\dfrac{64}{100}}$

$\Rightarrow$  $\dfrac{8}{10}$

$\Rightarrow$   $0.80$

$\therefore$    Square root of $64\%$ is $0.8.$

A reduction of 20% in the price of rice enables a person to buy 3.5 kg more for Rs. 77. Then the original price per kg is

  1. Rs. 4.00

  2. Rs. 4.50

  3. Rs. 5.00

  4. Rs. 5.50


Correct Option: D
Explanation:

Let the original price of rice be $Rs. x\ per\ kg$.


New price $=\dfrac{4x}{5}\ per\ kg$

According to the question,
$\dfrac{77}{\dfrac{4x}{5}}-\dfrac{77}{x}=3.5$
$\dfrac{385-308}{4x}=3.5$
$\dfrac{77}{4x}=3.5$
$x=\dfrac{77}{14}$
$x=Rs.5.5\ per\ kg$

Hence, this is the answer.

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