Tag: division of decimals

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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.

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

$54.327\times 357.2\times 0.0057$ 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
Given expression is $54.327\times 357.2\times 0.0057$
$\Rightarrow$  Number of decimal places in the given expression = $8$
$\Rightarrow$   Number of decimal places in (A) = 8
$\Rightarrow$   Number of decimal places in (B) = 9 
$\Rightarrow$   Number of decimal places in (C)= 7
$\therefore$    The expression in $(A)$ is the same as the given Expression.

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

Simplify $\left[\displaystyle\frac{(0.333)^3}{(0.111)^2}-\frac{(0.222)^4}{(0.111)^3}\right]$.

  1. $1.331$
  2. $1.221$
  3. $1.484$
  4. $1.551$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given, $[\dfrac{(0.333)^3}{(0.111)^2} - \dfrac{(0.222)^4}{(0.111)^3}]$
We can solve like 
= $[\dfrac{0.333 \times 0.333 \times 0.333}{0.111 \times 0.111} - \dfrac{0.222 \times 0.222 \times 0.222 \times 0.222}{0.111 \times 0.111 \times 0.111}]$
= ${3 \times 3 \times 0.333} - 2 \times  2 \times 2 \times 0.222$
= $2.997 - 1.776$
= $1.221$
Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

Find the product:
$\displaystyle 0.05\times 0.09\times 5$

  1. $0.025$
  2. $0.225$
  3. $0.005$
  4. $0.0225$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Multiply the numbers without decimal point
i.e. $5\times 9\times 5=225$
$0.05$ have decimal point after $2$ digits
$0.09$ have decimal point after $2$ digits
So, the product will have decimal point after $2+2=4$ digits
Thus, the product of $0.05\times 0.09 \times 5=0.0225$