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Conversion of fractions and decimals to percentages - class-VI

Description: conversion of fractions and decimals to percentages
Number of Questions: 30
Created by:
Tags: how much of hundred? percentages maths percentage comparing quantities using proportion calculations and mental strategies 3 comparing quantity percentage and simple interest comparing quantities percent comparison of quantities equivalence of fraction, decimal fraction, percentage and ratio
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$\dfrac{3}{5}$ as a percent is

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $30\%$

  2. $40\%$

  3. $45\%$

  4. $60\%$

Show answer
Correct Option: D
Explanation:

$\cfrac{3}{5}$ as a percent is$=\cfrac{3}{5}\times 100=60\%$

$6:5$ when expressed as a percentage is

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $83\dfrac{1}{3}\%$

  2. $90\%$

  3. $120\%$

  4. $6.5\%$

Show answer
Correct Option: C
Explanation:

$6:5$ as a percent is$=\cfrac{6}{5}\times 100=120\%$

Convert the given ratio to percentage.
$2:3$.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $60.67\%$

  2. $26.67\%$

  3. $66.67\%$

  4. None of these

Show answer
Correct Option: C
Explanation:

$(2:3)\%$

$=\cfrac{2}{3}\times100$

$=66.67\%$

A maths exam is marked out of $120$.Passing mark percentage is 40%.What are marks required for passing?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $48$

  2. $110$

  3. $54$

  4. $72$

Show answer
Correct Option: A
Explanation:

40% of 120 is 

$\dfrac{40}{100}*120=48$

Hence, passing marks are $48$

The ratio $2 :3$ expressed as percentage is 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $40|%$

  2. $60\%$

  3. $66\dfrac{2}{3}\%$

  4. $33\dfrac{1}{3}\%$

Show answer
Correct Option: C
Explanation:

$(2:3)\%=\cfrac{2}{3}\times 100=66.66\%$

Write as percentage $4\dfrac {4}{20}$

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $84\%$

  2. $420\%$

  3. $8.4\%$

  4. $42\%$

Show answer
Correct Option: B
Explanation:

$4\dfrac{4}{20}$

$\Rightarrow \dfrac{84}{20}\times 100\Rightarrow 420\%$

Find the fraction of $25$ paise to $Rs  2$.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $\dfrac{9}{8}$

  2. $\dfrac{3}{8}$

  3. $\dfrac{5}{8}$

  4. $\dfrac{1}{8}$

Show answer
Correct Option: D
Explanation:

Rs.1 is equal to 100 paise 

Rs 2 is equal to 200 paise
fraction of 25 paise to Rs 2 $=\dfrac{25paise}{200paise}$
                                              $=\dfrac{1}{8}$

The fraction $\dfrac{1}{5}$ converted to percentage is 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $20\% $

  2. $30\% $

  3. $40\% $

  4. $50\% $

Show answer
Correct Option: A
Explanation:

We have,

$\dfrac{1}{5}$


$\dfrac{1}{5} \%=\dfrac{1}{5}\times 100$

$\dfrac{1}{5}=20\%$


Hence, this is the answer.

$\dfrac{3}{4}$ means

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 75

  2. 75%

  3. $\dfrac{400}{3}$

  4. $\dfrac{400}{3}$%

Show answer
Correct Option: B
Explanation:

$\frac{3}{4} = \frac{3}{4} \times 100$ % = $75$%

$\frac{2}{5}$ of total students in a class have opted Maths.Find the percentage of students opting Maths

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $\frac{2}{5}\times 100$

  2. $\frac{5}{2}\times 100$

  3. $\frac{2}{5}\times \frac{1}{100}$

  4. $\frac{5}{2}\times \frac{1}{100}$

Show answer
Correct Option: A
Explanation:

Let total student be = $s$
$\frac{2}{5}$ of the students opt for Maths = $\frac{2s}{5}$
Percentage of students opting for maths = $\frac{\frac{2s}{5}}{s} \times 100 = \frac{2}{5} \times 100 = 40$ % of the students

$150$ is what percent of $30$?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $5\%$

  2. $20\%$

  3. $50\%$

  4. $200\%$

  5. $500\%$

Show answer
Correct Option: E
Explanation:

Let the percentage be $x$.

$\dfrac {100\%}{x\%}=\dfrac {30}{150}$
$\Rightarrow \dfrac {100}{x}\times x=\dfrac {30}{150}\times x$ .... Multiply both sides by $x$
$\Rightarrow 100=0.2x$
$\Rightarrow x=500$
Thus, $150$ is $500\%$ of $30$.

If A exceeds B by $40$ %, B is less than C by $20$% , then A : C is :

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $28:25$

  2. $26:25$

  3. $283:251$

  4. $287:254$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Let $C = 100.$

$\Rightarrow$   So B = 20% less than C or 80% of C = $\dfrac{80}{100}\times 100=80$
$\Rightarrow$  So, A = B + 40% of B
$\Rightarrow$   $A=80+80\times \dfrac{40}{100}=112$

$\therefore$   $A:C=\dfrac{A}{C}=\dfrac{112}{100}=\dfrac{28}{25}$

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

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $37.5\%$

  2. $37\%$

  3. $34.5\%$

  4. $25\%$

Show answer
Correct Option: A
Explanation:

We have to find percent of $\dfrac{3}{8}$

$\text{Percentage}=\left (\dfrac{3}{8}\times 100\right)\%$
Therefore, $\text{Percentage}=37.5\%$

What percentage is equivalent to $\dfrac {5}{8}$ ?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $62.5\%$

  2. $60.5\%$

  3. $625\%$

  4. $60\%$

Show answer
Correct Option: A
Explanation:

We have to find percentage of $\dfrac{5}{8}$

We know $\text{Percentage} = \dfrac{5}{8}\times 100$
Therefore, $\text{Percentage} = \dfrac{500}{8}=62.5\%$

Convert $\dfrac{46}{5}$ into percentage.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $92 \%$

  2. $920\%$

  3. $9.2\%$

  4. $0.92\%$

Show answer
Correct Option: B
Explanation:

The fraction in percentage equals

$\dfrac { 46 }{ 5 } \times 100=920\%$
So, option B is correct.

Amar wrote exams in four subjects-Physics, Chemistry, Biology and Social Studies. The ratio of marks he got in these exams was $2:3:4:5$. He got an aggregate of 70% in these exams. Each exam had the same maximum marks. In how many of these exams did he get more than 50%?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: C
Explanation:

Let the maximum marks of each subject $= y$

Let the marks scored in Physics, Chemistry, Biology and social studies be $2x, \,3x, \,4x$ and $5x$.
Now, total marks scored in all 4 subjects $2x+3x+4x+5x = 14x$
Total maximum marks of all 4 subjects $=4y$
Now according to question:
$\left(\dfrac{14x}{4y}\times 100\right)\% = 70\%$
$\Rightarrow \dfrac{14x}{4y}\times 100 = 70$
$\Rightarrow y = 5x$
$\%$ age of marks scored in Physics $=\left(\dfrac{2x}{5x} \times 100\right)\% = 40\%$ 
$\%$ age of marks scored in Chemistry $=\left(\dfrac{3x}{5x} \times 100\right)\% = 60\%$ 
$\%$ age of marks scored in Biology $=\left(\dfrac{4x}{5x} \times 100\right)\% = 80\%$
$\%$ age of marks scored in Social Studies $=\left(\dfrac{5x}{5x} \times 100\right)\% = 100\%$  
So, he got more than $50\%$ in Chemistry, Biology and Social Studies.
Hence, the answer is $3$.

270 candidates appeared for an examination, of which 252 passed. The pass percentage is? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $80 \%$

  2. $83 \frac { 1 } { 2 } \%$

  3. $90 \frac { 1 } { 3 } \%$

  4. $93 \frac { 1 } { 3 } \%$

Show answer
Correct Option: D
Explanation:

Total candidates = 270

Passes candidates = 252
Passed percentage = $\dfrac{252}{270} \times 100\%=93.33\%=93\dfrac{1}{3}\%$

Which one of the following shows the best percentage? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $\dfrac { 384 } { 540 }$

  2. $\dfrac { 425 } { 500 }$

  3. $\dfrac { 570 } { 700 }$

  4. $\dfrac { 480 } { 660 }$

Show answer
Correct Option: B
Explanation:
$(a)\dfrac{384}{540}=\dfrac{384}{540}\times 100\%=71\dfrac{1}{9}\%$

$(b)\dfrac{425}{500}=\dfrac{425}{500}\times 100\%=85\%$

$(c)\dfrac{570}{700}=\dfrac{570}{700}\times 100\%=81\dfrac{3}{7}\%$

$(d)\dfrac{480}{660}=\dfrac{480}{660}\times 100\%=72\dfrac{8}{11}\%$

$\dfrac{425}{500}$ shows the best percentage.

What percent of a day is 3 hours? 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $12 \frac { 1 } { 2 } \%$

  2. $16 \frac { 1 } { 3 } \%$

  3. $18 \frac { 2 } { 3 } \%$

  4. $22 \frac { 1 } { 2 } \%$

Show answer
Correct Option: A
Explanation:

No . of hours in a day $24hours$

Percentage of $3$ hrs is given as 

$\dfrac{3}{24}\times 100$

$\dfrac 18\times 100=12\frac 12\%$

Express the following ratios as percentages: 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 5 : 4

  2. 1 : 1

  3. 2 : 3

  4. 9 : 16

Show answer
Correct Option: A

Express the following percentages as ratios in the reduced form.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 75 : 100

  2. 44 : 100

  3. 6.25%

  4. 52 : 100

    1. 64%
Show answer
Correct Option: A

Each side of the cube is increased by 50%.Then the surface area of the cube is increased by 

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 50%

  2. 100%

  3. 125%

  4. 150%

Show answer
Correct Option: C
Explanation:

Let each side be $1.5l$ (after increase).Then % increase in surface area
    =$\displaystyle\frac{13.5{l}^{2}-6{l}^{2}}{6{l}^{2}}\times 100$ =125 %

Equivalent of $\displaystyle \frac { 6 }{ 20 } $ is:

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $6 \%$

  2. $20 \%$

  3. $26 \%$

  4. $30 \%$

Show answer
Correct Option: D
Explanation:
$\dfrac{6}{20}$$=\dfrac{6}{20} \times 100$ $=30\%$

The fraction $\dfrac {x}{y}$ is altered by decreasing $x$ by $25$ per cent and increasing $y$ by $25$ percent. The new fraction is what percent less than the original?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. 35

  2. 40

  3. 42

  4. 45

Show answer
Correct Option: B
Explanation:

Let the fraction is $=\dfrac{x}{y}$

If we decrease $x$ by $25\%$, then the $x=.75x$
If we increase $y$ by $25 \%$,  then the $y=1.25y$
$\therefore$ new fraction is $=\dfrac{.75x}{1.25y}=0.6\dfrac{x}{y}$
So, the new fraction is $0.4$ or $40\%$ less than the original fraction.

Convert $\dfrac{16}{50}$ into percentage.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $32\%$

  2. $34\%$

  3. $36\%$

  4. $38\%$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  We have to convert $\dfrac{16}{50}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{16}{50}\times 100)\%$

$\Rightarrow$  $\%=(16\times 2)\%$

$\therefore$    $\%=32\%$

Convert $\dfrac{14}{25}$ into percentage

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $55\%$

  2. $56\%$

  3. $57\%$

  4. $58\%$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  We have to convert $\dfrac{14}{25}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{14}{25}\times 100)\%$

$\Rightarrow$  $\%=(14\times 4)\%$

$\therefore$    $\%=56\%$

Convert $\dfrac{15}{50}$ into percentage

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $35\%$

  2. $30\%$

  3. $25\%$

  4. $20\%$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  We have to convert $\dfrac{15}{50}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{15}{50}\times 100)\%$

$\Rightarrow$  $\%=(15\times 2)\%$

$\therefore$    $\%=30\%$

In a survey, one in six people said they preferred a particular brand of cola. What this fraction is? And convert this fraction into percentage.

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $25\%$

  2. $17\%$

  3. $10\%$

  4. $5\%$

Show answer
Correct Option: B
Explanation:

One in six people means $\dfrac{1}{6}$ people in fraction.


To convert a fraction into percentage, multiply it by $100$
$\therefore \dfrac{1}{6} = \dfrac{1}{6} \times 100 = 16.67\% \approx 17\%$

When Rani was buying her flat she had to put down a deposit of $\dfrac{1}{10}$ of the value of the flat. What percentage was this?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $10\%$

  2. $20\%$

  3. $30\%$

  4. $1\%$

Show answer
Correct Option: A
Explanation:

To convert a fraction into percentage, simply multiply it by $100$

So, $\dfrac{1}{10}$ of the value of the flat in percentage is $\dfrac{1}{10} \times 100 = 10\%$

I bought my coat in the January sales with $\dfrac{1}{3}$ off the original price. What percentage was taken off the price of the coat?

maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

  1. $11\%$

  2. $22\%$

  3. $33\%$

  4. $44\%$

Show answer
Correct Option: C
Explanation:

Coat was bought at rate $\dfrac{1}{3}$ off the original price

Converting into percentage, $\dfrac{1}{3} \times 100 = 33.33\%$ was taken off the price of coat.

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