Tag: calculating and mental strategies 3

Quizzes (11) Questions (95)

Questions Related to calculating and mental strategies 3

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

The result of $(54.327\times 357.2\times 0.0057)$ is the same as

  1. $5.4327\times 3.572\times 5.7$
  2. $5.4327\times 3.572\times 0.57$
  3. $54327\times 3572\times 0.0000057$
  4. $5432.7\times 3.572\times 0.000057$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$54.327 \times 357.2 \times 0.0057 = \cfrac {54327}{1000} \times \cfrac {3572}{10} \times \cfrac {57}{10000}$

                                             $= \cfrac {54327}{1000} \times \cfrac {10}{10} \times \cfrac {3572}{10} \times \cfrac {100}{100} \times \cfrac {57}{10000} \times \cfrac {1000}{1000}$
                                             $= \cfrac {54327}{10000} \times 10 \times \cfrac {3572}{1000} \times 100 \times \cfrac {57}{10000} \times \cfrac {1000}{1000}$

                                           $= 5.4327 \times 3.572 \times 5.7 \times 10 \times 100 \times \cfrac {1}{1000}$
                                           $= 5.4327 \times 3.572 \times 5.7$

Hence, option A is correct.

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

Evaluate : $\displaystyle \frac{0.0203\times2.92}{0.0073\times14.5\times0.7}$

  1. $0.2$
  2. $0.3$
  3. $0.6$
  4. $0.8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We will first convert the decimals into fraction in the given fraction and then solve it as follows:


$\dfrac { 0.0203\times 2.92 }{ 0.0073\times 14.5\times 0.7 } =\dfrac { \dfrac { 203 }{ 10000 } \times \dfrac { 292 }{ 100 }  }{ \dfrac { 73 }{ 10000 } \times \dfrac { 145 }{ 10 } \times \dfrac { 7 }{ 10 }  }$

$ =\dfrac { \dfrac { 203\times 292 }{ 1000000 }  }{ \dfrac { 73\times 145\times 7 }{ 1000000 }  } =\dfrac { 203\times 292 }{ 73\times 145\times 7 }$

$=\dfrac{29\times 7 \times 73\times4}{73\times 29\times 5\times 7} =\dfrac { 4 }{ 5 } =0.8$

Hence, $\dfrac { 0.0203\times 2.92 }{ 0.0073\times 14.5\times 0.7 } =0.8$

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

If $\sqrt{.04\times .4\times a} = .004\times .4\times \sqrt{b}$, then $\dfrac{a}{b}$ is 

  1. $16\times 10^{-3}$
  2. $16\times 10^{-4}$
  3. $16\times 10^{-5}$
  4. $16\times 10^{-6}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\sqrt{0.4\times 0.04\times a}=0.004\times 0.4\times \sqrt{b}$ 

$\Rightarrow \sqrt{\dfrac{a}{b}}=\dfrac{0.004\times 0.4}{\sqrt{0.4\times 0.04}}=\dfrac{16\times 10^{-4}}{4\times 10^{-1-5}}$ 
$\Rightarrow \dfrac{a}{b}=(4\times 10^{25})^{2}=\boxed{16\times 10^{-5}}$

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

The value of $\dfrac { { \left( 0.96 \right)  }^{ 3 }-{ \left( 0.1 \right)  }^{ 3 } }{ { \left( 0.96 \right)  }^{ 2 }+0.096+{ \left( 0.1 \right)  }^{ 2 } } $ is:

  1. $0.86$
  2. $0.95$
  3. $0.97$
  4. $1.06$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given expression $=\dfrac { { \left( 0.96 \right)  }^{ 3 }-{ \left( 0.1 \right)  }^{ 3 } }{ { \left( 0.96 \right)  }^{ 2 }+\left( 0.96\times 0.1 \right) +{ \left( 0.1 \right)  }^{ 2 } } $
                             $=\left( \dfrac { { a }^{ 3 }-{ b }^{ 3 } }{ { a }^{ 2 }+ab+{ b }^{ 2 } }  \right) $
                             $=\left( a-b \right) $
                             $=\left( 0.96-0.1 \right) $
                             $= 0.86$

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

If $x = 16.2357$, then $\dfrac{x}{10} = $

  1. $162.357$
  2. $1.62357$
  3. $16.2357$
  4. $0.162357$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that in general, $\dfrac {1}{10}=0.1$.


It is given that $x=16.2357$, then $\dfrac {x}{10}$ will be as follows:

$\dfrac { x }{ 10 } =\dfrac { 16.2357 }{ 10 } =16.2357\times 0.1=1.62357$


Hence, $\dfrac { x }{ 10 } =1.62357$

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

If a decimal number is divided by $1000$, then the decimal point shifts to the _____ by _____ positions.
(Fill in the blanks respectively from the options given below)

  1. left, $2$
  2. right. $3$
  3. left, $3$
  4. right. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When we divide a decimal number by $1000$, we move all the digits three places to the right and the number becomes thousand times smaller. For example:


$\dfrac {3502.0}{1000}=3.502$ where the decimal point shifts to the left by $3$ positions.

Hence, if a decimal number is divided by $1000$, then the decimal point shifts to the left by $3$ positions.