Tag: decimal numbers

Questions Related to decimal numbers

The value of $0.\overline{1}+0.0\overline{1}+0.00\overline{1}$ is equal to

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $\dfrac{343}{900}$

  2. $\dfrac{37}{300}$

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

  4. $\dfrac{1343}{10989}$

Show answer
Correct Option: B
Explanation:
Let $  x = 0.\bar{1} \Rightarrow 10x = 1.\bar{1}$

$ 10x -x = 1 \Rightarrow  x = 1/9 ...(I)$

$ y = 0.0\bar{1} = 0.01+0.001+0.0001+...$

$ = \dfrac{1}{100}+\dfrac{1}{1000}+\dfrac{1}{10000}+...$

$ = \dfrac{1}{100}(1+\dfrac{1}{10}+\dfrac{1}{100}+...)$

$ = \dfrac{1}{100}\times \dfrac{1}{1-\dfrac{1}{10}} = \dfrac{1}{90}...(II)$

$ z = 0.00\bar{1} = 0.001+0.0001 + 0.00001+...$

$=0.001(1+\dfrac{1}{10}+\dfrac{1}{100}+...)$

$ =\dfrac{1}{1000}\times \dfrac{1}{1-\frac{1}{10}}  = \dfrac{1}{1000} \times \dfrac{10}{9} = \dfrac{1}{900}...(III)$

From (1),(2),(3) $ 0.\bar{1}+0.0\bar{1}+0.00\bar{1} = \dfrac{1}{9}+\dfrac{1}{90}+\dfrac{1}{900}= \dfrac{111}{900} = \dfrac{37}{300}$

$ \therefore $ option B is correct

The width of the class  $55.5 - 60.5$  is

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $10$

  2. $5$

  3. $2.5$

  4. $7$

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Correct Option: B
Explanation:

Width of class $=U.L-L.L=60.5-55.5=5$

A flask weighs $64.27\,g$ when empty and $150.35\,g$ when full of water, Find the wight when it is $0.75$ times full of water.

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $128.83\,g$

  2. $120\,g$

  3. $150\,g$

  4. $73.3\,g$

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Correct Option: A

Vanmathi bought $4$ books each weighing $500\ g$. The weight of $4$ books is $2\ kg$.

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. True

  2. False

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Correct Option: A

Simplify the following :

$0.4 \times \displaystyle \frac{7}{3} \div \frac{15}{8}  $ of $  \left ( \dfrac{7}{5} - \dfrac{4}{3} \right )$.

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $\displaystyle 5 \frac{8}{3375}$

  2. $\displaystyle 7 \frac{8}{15}$

  3. $\displaystyle 7 \frac{7}{15}$

  4. $\displaystyle 5 \frac{7}{3375}$

Show answer
Correct Option: C
Explanation:

The given expression is

$0.4\times \dfrac { 7 }{ 3 } \div \dfrac { 15 }{ 8 } $ of $\left( \dfrac { 7 }{ 5 } -\dfrac { 4 }{ 3 }  \right) $

$=\dfrac { 4 }{ 10 } \times \dfrac { 7 }{ 3 } \div \dfrac { 15 }{ 8 } $ of $\dfrac { 1 }{ 15 } $

$ =\dfrac { 2 }{ 5 } \times \dfrac { 7 }{ 3 } \div \dfrac { 1 }{ 8 } $

$ =\dfrac { 2 }{ 5 } \times \dfrac { 7 }{ 3 } \times \dfrac { 8 }{ 1 } $

$ =\dfrac { 112 }{ 15 } $

$=7\dfrac { 7 }{ 15 } $

The simplification of
$2.002+7.9\left{ 2.8-6.3\left( 3.6-1.5 \right) +15.6 \right} $ yields

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. 2.002

  2. 4.2845

  3. 40.843

  4. 42.845

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Correct Option: D
Explanation:

$2.002+7.9\left{ 2.8-6.3\left( 3.6-1.5 \right) +15.6 \right} $
$=2.002+7.9\left{ 2.8-6.3\times 2.1+15.6 \right} $
$=2.002+7.9\left{ 2.8-13.23+15.6 \right} $
$=2.002+7.9\left{ 5.17 \right} $
$=2.002+40.843=42.845$

Solve : $25 +\displaystyle{\frac{3}{100}}+\displaystyle{\frac{4}{1000}}=$ ?

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $25.34$

  2. $25.304$

  3. $25.034$

  4. $25.0034$

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Correct Option: C
Explanation:

The value of $25 $ $+$ $\displaystyle{\frac{3}{100}}$ $+$ $\displaystyle{\frac{4}{1000}}$ is

$=25+0.03+0.004$
$= 25.034$

Which number is equal to $\displaystyle{\left(\frac{0.1}{0.01} + \frac{0.01}{0.1}\right)}$ ?

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $10.1$

  2. $1.10$

  3. $1.01$

  4. $10.01$

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Correct Option: A
Explanation:

$\displaystyle{\frac{0.1}{0.01} + \frac{0.01}{0.1}}$ = 10 + $\displaystyle{\frac{1}{10}}$ $= 10 + 0.1 = 10.1$

3 tens 6 thousandths is

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $30.6$

  2. $30.06$

  3. $310.6000$

  4. $30.006$

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Correct Option: D
Explanation:

3 tens 6 thousandths is

$=30+\dfrac{6}{1000}=30+0.006=30.006$

$58 +\displaystyle{\frac{3}{100}}+\displaystyle{\frac{7}{1000}}=?$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $58.0037$

  2. $58.37$

  3. $58.037$

  4. none

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Correct Option: C