Tag: written methods

Questions Related to written methods

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

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

  1. $16\times 10^{-3}$

  2. $16\times 10^{-4}$

  3. $16\times 10^{-5}$

  4. $16\times 10^{-6}$

Show answer
Correct Option: C
Explanation:

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

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

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:

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

  1. $0.86$

  2. $0.95$

  3. $0.97$

  4. $1.06$

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Correct Option: A
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) $
                             $= 0.86$

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

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

  1. $162.357$

  2. $1.62357$

  3. $16.2357$

  4. $0.162357$

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Correct Option: B
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, $\dfrac { x }{ 10 } =1.62357$

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)

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

  1. left, $2$

  2. right. $3$

  3. left, $3$

  4. right. $2$

Show answer
Correct Option: C
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.

Perform division of numbers:
$1234.46\div8$

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

  1. $15430.75$

  2. $15403.075$

  3. $154.3075$

  4. $15.43075$

Show answer
Correct Option: C
Explanation:
Multiplying and dividing by $100$ we get
$1234.46\div 8 = (123446\div 8)\div100$
                    $=154.3075$

Fill in the banks: 

$425$ paise $=$ Rs._____

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

  1. $4.25$

  2. $42.5$

  3. $4.5$

  4. $2.5$

Show answer
Correct Option: A
Explanation:

As we know $1$ Rs $= 100$ paisa


So, 425 paisa = $\dfrac{425}{100}$ Rs


$= 4.25$ Rs

$54.327\times 357.2\times 0.0057$ is the same as.

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

  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. $5432.7\times 3.572\times 0.000057$

Show answer
Correct Option: A
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.

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

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

  1. $1.331$

  2. $1.221$

  3. $1.484$

  4. $1.551$

Show answer
Correct Option: B
Explanation:
Given, $[\dfrac{(0.333)^3}{(0.111)^2} - \dfrac{(0.222)^4}{(0.111)^3}]$
We can solve like 
= $[\dfrac{0.333 \times 0.333 \times 0.333}{0.111 \times 0.111} - \dfrac{0.222 \times 0.222 \times 0.222 \times 0.222}{0.111 \times 0.111 \times 0.111}]$
= ${3 \times 3 \times 0.333} - 2 \times  2 \times 2 \times 0.222$
= $2.997 - 1.776$
= $1.221$

Divide $125.625$ by $0.5$

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

  1. $251.25$

  2. $2512.5$

  3. $25125$

  4. $25.125$

Show answer
Correct Option: A
Explanation:

Division of $125.625$ by $0.5$ is

$\dfrac{125.625}{0.5}$ $=251.25$
Hence, the answer is $251.25$

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

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

  1. $0.025$

  2. $0.225$

  3. $0.005$

  4. $0.0225$

Show answer
Correct Option: D
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 $0.05\times 0.09 \times 5=0.0225$