Tag: decimal numbers

Quizzes (12) Questions (85)

Questions Related to decimal numbers

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

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

  1. $\dfrac{343}{900}$
  2. $\dfrac{37}{300}$
  3. $\dfrac{4}{33}$
  4. $\dfrac{1343}{10989}$
Reveal answer Fill a bubble to check yourself
B Correct answer
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
Multiple choice maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

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.

  1. $128.83\,g$
  2. $120\,g$
  3. $150\,g$
  4. $73.3\,g$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The weight of the water alone is 150.35g - 64.27g = 86.08g. If the flask is 0.75 times full, the water weighs 0.75 * 86.08g = 64.56g. Adding the empty flask weight (64.27g) gives 128.83g.

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

Simplify the following :

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

  1. $\displaystyle 5 \frac{8}{3375}$
  2. $\displaystyle 7 \frac{8}{15}$
  3. $\displaystyle 7 \frac{7}{15}$
  4. $\displaystyle 5 \frac{7}{3375}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 } $

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

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

  1. 2.002

  2. 4.2845

  3. 40.843

  4. 42.845
Reveal answer Fill a bubble to check yourself
D Correct answer
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} $
$=2.002+40.843=42.845$