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

The value of $(1.02)^4+(0.98)^4$ upto three places of decimal is

  1. $2.004$
  2. $2.003$
  3. $2.04$
  4. $2.0004$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${\left( 1.02 \right)}^{4} + {\left( 0.98 \right)}^{4}$

$= {\left( 1 + 0.02 \right)}^{4} + {\left( 1 - 0.02 \right)}^{4}$
$= \left[ {^{4}{C} _{0}} {\left( 1 \right)}^{4} + {^{4}{C} _{1}} {\left( 1 \right)}^{4-1} {\left( 0.02 \right)}^{1} + {^{4}{C} _{2}} {\left( 1 \right)}^{4-2} {\left( 0.02 \right)}^{2} + {^{4}{C} _{3}} {\left( 1 \right)}^{4-3} {\left( 0.02 \right)}^{3} + {^{4}{C} _{4}} {\left( 1 \right)}^{4-4} {\left( 0.02 \right)}^{4} \right] + \ \left[ {^{4}{C} _{0}} {\left( 1 \right)}^{4} - {^{4}{C} _{1}} {\left( 1 \right)}^{4-1} {\left( 0.02 \right)}^{1} + {^{4}{C} _{2}} {\left( 1 \right)}^{4-2} {\left( 0.02 \right)}^{2} - {^{4}{C} _{3}} {\left( 1 \right)}^{4-3} {\left( 0.02 \right)}^{3} + {^{4}{C} _{4}} {\left( 1 \right)}^{4-4} {\left( 0.02 \right)}^{4} \right]$
$= 2 \left[ {^{4}{C} _{0}} + {^{4}{C} _{2}} \left( 0.0004 \right) + {^{4}{C} _{4}} \left( 0.00000016 \right) \right]$
$= 2 \times \left( 1 + 0.0024 + 0.00000016 \right)$
$= 2 \times 1.002$
$= 2.004$
Hence the value of given expression upto three places of decimal is $2.004$.

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} $
$=2.002+40.843=42.845$