Tag: calculating and mental strategies 3

Questions Related to calculating and mental strategies 3

The result of $(54.327\times 357.2\times 0.0057)$ 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. $5432.7\times 3.572\times 0.000057$

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Correct Option: A
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.

Lakshmi is 150 cm tall. What is her height in metres ? 

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

  1. $1$ metre

  2. $1.5$ metres

  3. $15.0$ metres

  4. $0.15$ metres

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Correct Option: B
Explanation:
Given Lakshmi is $150\ cm$ tall

$1m=100cm\Rightarrow 1cm=\dfrac{1}{100}m$

$\therefore150\ cm =$ $\displaystyle{\frac{150}{100}}$ $= 1.5\ m$

$\therefore$  Lakshmi is $1.5\ m$ tall

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

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

  1. $0.2$

  2. $0.3$

  3. $0.6$

  4. $0.8$

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Correct Option: D
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, $\dfrac { 0.0203\times 2.92 }{ 0.0073\times 14.5\times 0.7 } =0.8$

Which integer values of $j$ would give the number $-37,129 \times 10^j$ a value between -100 and -1?

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

  1. (-1,-2)

  2. (-3,-4)

  3. (-2,-3)

  4. (-4,-5)

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Correct Option: B
Explanation:

The number can take value 3.7129 to 37.129. And this can be obtained by multiplying by $10^{-3} or 10^{-4}$ to the given number. 

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

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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