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Converting decimals to fractions and vice-versa - class-V

Description: converting decimals to fractions and vice-versa
Number of Questions: 17
Created by:
Tags: decimal fractions addition, subtraction and multiplication of fractions maths
Attempted 0/17 Correct 0 Score 0

Convert $0.25$ into fraction.

  1. $\displaystyle \frac{3}{4}$

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

  3. $\displaystyle \frac{1}{4}$

  4. none of the above


Correct Option: C
Explanation:

$0.25=\displaystyle \frac{25}{100}=\frac{1}{4}$

Convert $0.55$ in to a fraction.

  1. $\displaystyle \frac{11}{20}$

  2. $\displaystyle \frac{2}{9}$

  3. $\displaystyle \frac{3}{9}$

  4. $\displaystyle \frac{4}{9}$


Correct Option: A
Explanation:

$0.55=\displaystyle \frac{55}{100}=\frac{11}{20}$

$0.8$ can be represented as

  1. $\displaystyle \frac{8}{10}$

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

  3. $\displaystyle \frac{8}{1000}$

  4. None of the above


Correct Option: A
Explanation:

Multiplying the numerator and denominator by $10$ we get,
$0.8=\displaystyle \frac{8}{10}$

$\displaystyle \frac{0.25}{0.4}$ is equal to

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

  2. $\displaystyle \frac{25}{40}$

  3. $\displaystyle \frac{16}{19}$

  4. None of the above


Correct Option: A,B
Explanation:
$\dfrac {0.25}{0.4}$ = $\dfrac{\dfrac {25}{100}}{ \dfrac {4}{10}}$

$= \displaystyle \frac{25\times 10}{4 \times 100} = \frac{25}{40}$

So. options A and B are correct.

In the number $0.257$, which of the following does the digit $7$ represent?

  1. $\displaystyle 7\times\frac{1}{10}$

  2. $\displaystyle 7\times\frac{1}{100}$

  3. $\displaystyle 7\times\frac{1}{1000}$

  4. $\displaystyle 7\times\frac{1}{10000}$

  5. $\displaystyle 7\times\frac{1}{100000}$


Correct Option: C
Explanation:

The number $0.257$ can be represented as $0.2 + 0.05 + 0.007$.

Therefore we can see that digit $7$ represents $0.007 = 7\times \dfrac { 1 }{ 1000 } $.

$0.614$ can be represented as 

  1. $\displaystyle \frac{61.4}{10}$

  2. $\displaystyle \frac{614}{1000}$

  3. $\displaystyle \frac{614}{10}$

  4. None of the above


Correct Option: B
Explanation:

$0.614 =\displaystyle \frac{614}{1000}$


So, option B is correct.

Express the following as a fraction and simplify:

$0.008$

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

  2. $\cfrac {1}{125}$

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

  4. $\cfrac {4}{125}$


Correct Option: B
Explanation:

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:
$0.008= \cfrac{8}{1000} = \cfrac{1}{125}$

$0.43$ is rational and it can be written as ..........

  1. $\dfrac {43}{100}$

  2. $\dfrac {43}{10}$

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

  4. $\dfrac {34}{10}$


Correct Option: A
Explanation:

$0.43 = \dfrac {43}{100}$ (As it is expressed a fraction.)
Therefore, $A$ is the correct answer.

$0.34$ can be represented as

  1. $\displaystyle \frac{34}{100}$

  2. $\displaystyle \frac{34}{1000}$

  3. $\displaystyle \frac{34}{10}$

  4. None of the above


Correct Option: A
Explanation:

$0.34 =\displaystyle \frac{34}{100}$


So, option A is correct.

$\dfrac {p}{q}$ form of $0.0875$ is _______

  1. $\dfrac {7}{2^{4}\times 5}$

  2. $\dfrac {7}{2\times 5^{4}}$

  3. $\dfrac {7}{2^{4}\times 5^{4}}$

  4. $\dfrac {5^{3}\times 7}{2^{3}\times 5^{4}}$


Correct Option: A
Explanation:

Since, $0.0875=\displaystyle \frac {875}{10000}=\frac {175}{2000}=\frac{35}{400} =\frac {7}{80}=\frac 7{16\times 5}=\frac 7{2^4\times 5}$

Option $A$ is correct.

0.585 is equal to

  1. $\frac{589}{100}$

  2. $\frac{585}{1000}$

  3. $\frac{1000}{585}$

  4. None of these


Correct Option: B
Explanation:

$0.585 = 0.5+0.08+0.005 = \dfrac{5}{10} + \dfrac{8}{100} + \dfrac{5}{1000}$
$0.585 = \dfrac{585}{1000}$

$0.2008$ is equal to

  1. $\dfrac {252}{1250}$

  2. $\dfrac {251}{1250}$

  3. $\dfrac {250}{1250}$

  4. None of these


Correct Option: B
Explanation:

$\dfrac {2008}{1000} = \dfrac {1004}{500}$


$= \dfrac {502}{250}$$= \dfrac {251}{125}$

So, option $B$ is correct.

Convert the following into a fraction:

$0.2\times 0.02\times 0.002$

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

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

  3. $\dfrac {1}{125000}$

  4. None of these


Correct Option: C
Explanation:

$\dfrac {2}{10}\times \dfrac {2}{100} \times \dfrac {2}{1000}$

$= \dfrac {8}{10\times 100\times 1000}$

$= \dfrac {4}{5\times 100\times 1000}$

$= \dfrac {1}{125000}$

So, option $C$ is correct.

$2.\overline{8768}$  expressed as a rational number is 

  1. $\displaystyle 2\frac{878}{999}$

  2. $\displaystyle 2 _{10}^{9}$

  3. $\displaystyle 2\frac{292}{333}$

  4. $\displaystyle 2\frac{4394}{4995}$


Correct Option: C
Explanation:

$\displaystyle 2.\overline{8768}=2+0.\overline{8768}$
= $\displaystyle 2+\frac{8768-8}{9990}=2+\frac{8760}{9990}$
= $\displaystyle 2+\frac{292}{333}=2\frac{292}{333}$

Express the following as a fraction and simplify:

$2.45$

  1. $\cfrac {49}{20}$

  2. $\cfrac {20}{49}$

  3. $\cfrac {19}{20}$

  4. $\cfrac {20}{19}$


Correct Option: A
Explanation:

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:
$2.45 = 2\cfrac{45}{100} = 2\cfrac{9}{20}$    ...Mixed fraction

$=\cfrac{49}{20}$     ....Improper fraction

The decimal number $53.234$ is a rational number whose denominator is ............

  1. $100000$

  2. $10000$

  3. $1000$

  4. $100$


Correct Option: C
Explanation:

$53.234 = \dfrac {53234}{1000} = \dfrac {53234}{10^{3}}$
Denominator is $1000$.
Therefore, $C$ is the correct answer.

Express the infinite decimal .212121 as a common fraction.

  1. $\frac{21}{100}$

  2. $\frac{23}{99}$

  3. $\frac{7}{100}$

  4. $\frac{7}{99}$

  5. $\frac{7}{33}$


Correct Option: E
Explanation:

$Let\quad x=0.212121...\ 100x=21.212121....\ 100x-x=21\ 99x=21\ x=\frac { 21 }{ 99 } =\frac { 7 }{ 33 } $

So correct answer will be option E

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