Tag: written methods

Questions Related to written methods

Solve the following:
$44.3\div 10$


Ans : $4.43$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given, $44.3\div 10$


Could be written as,


$= \dfrac{443}{10}\times \dfrac{1}{10}$

$= \dfrac{443}{100}$

$= 4.43$
So, given statement is true.

Solve the following:
$2.3\div 100$


Ans : $0.023$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given, $23\div 100$


Could be written as,


$= 23\times \dfrac{1}{100}$

$= \dfrac{23}{100}$

$= 0.23$

So, given statement is false.

Which number is equal to $\left(\displaystyle\frac{0.1}{0.01}+\frac{0.01}{0.1}\right)$?

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

  1. $10.1$

  2. $1.10$

  3. $1.01$

  4. $10.0$

Show answer
Correct Option: A
Explanation:
Given, $\left(\displaystyle\frac{0.1}{0.01}+\frac{0.01}{0.1}\right)$
= $(10 + 0.1)$
= $10.1$

0.99 x = 100, then x = ?

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

  1. $101.01$

  2. $11.01$

  3. $101. \overline{01}$

  4. $11.\overline{01}$

Show answer
Correct Option: A

Express the following decimal in the form $\dfrac{p}{q}$: 

$0.\overline{37}$

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

  1. $\dfrac{37}{99}$

  2. $\dfrac{370}{99}$

  3. $\dfrac{37}{999}$

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$0.\bar {37}$

Let $x=0.37777$.....(1)

$100x=37.7777$.........(2)

(2)-(1) gives,

$99x=37$

$\therefore x=\dfrac{37}{99}$

Express the following decimal in the form $\dfrac{p}{q}$: 

$0.\overline{621}$

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

  1. $\dfrac{23}{37}$

  2. $\dfrac{230}{37}$

  3. $\dfrac{23}{370}$

  4. None of the above

Show answer
Correct Option: A
Explanation:
Given,

$0.\bar{621}$

Let $x=0.621621$.....(1)

$1000x=621.621$.........(2)

(2)-(1) gives,

$999x=621$

$\therefore x=\dfrac{69}{111}$

$\Rightarrow x=\dfrac{23}{37}$

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. $5432.7\times 3.572\times 0.000057$

Show answer
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

Show answer
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. $0.8$

Show answer
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)

Show answer
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.