Tag: calculating and mental strategies 3

Questions Related to calculating and mental strategies 3

$58+\frac {3}{100}+\frac {7}{1000}= ......$

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

  1. 58.0037

  2. 58.37

  3. 58.037

  4. none of these

Show answer
Correct Option: C
Explanation:

$58+\frac {3}{100}+\frac {7}{1000}$
$=58+\frac {0}{10}+\frac {3}{100}+\frac {7}{1000}=58.037$

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of $\displaystyle \left( { 10 }^{ 4 }-{ 10 }^{ 2 } \right) \left( 0.00\overline { 12 }  \right) $

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

  1. 0

  2. $\displaystyle 0.\overline { 12 } $

  3. 1.2

  4. 10

  5. 12

Show answer
Correct Option: E
Explanation:

$\displaystyle \left( { 10 }^{ 4 }-{ 10 }^{ 2 } \right) \left( 0.00\overline { 12 }  \right) $

= $ 9900 \times $ $0.00\overline{12}$
= $ 99 $ $\times$ $0.\overline{12}$..................(1)
Also, we know that
$ 0.\overline{12} $ = X
$ 12.\overline{12}$= 100X
Thus, 99X = 12 or X = $\cfrac{12}{99}$
So, (1) becomes
$99 \times \cfrac{12}{99} = 12$ So, option E

Rename the following decimals as percents.
$13.02$

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

  1. $1,30.2$ $\%$

  2. $1,3.02$ $\%$

  3. $1,302$ $\%$

  4. $1,3020$ $\%$

Show answer
Correct Option: C
Explanation:

$13.02 = \dfrac{1302}{100}$


When we talk about percents, we should multiply the number with $100$

So, the given decimal in percents is $\dfrac{1302}{100} \times 100 = 1302$ $\%$

Rename the following decimals as percents.
$0.374$

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

  1. $0.0374\%$

  2. $3.74\%$

  3. $37.4\%$

  4. $374\%$

Show answer
Correct Option: C
Explanation:

$0.374 = \dfrac{374}{1000}$


When we talk about percents, we should multiply the number with $100$
.
So the given decimal in percents is $\dfrac{374}{1000} \times 100 = \dfrac{374}{10} = 37.4$ $\%$

Which one of the following is a non-terminating and repeating decimal?

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

  1. $\dfrac {13}{8}$

  2. $\dfrac {3}{16}$

  3. $\dfrac {3}{11}$

  4. $\dfrac {137}{25}$

Show answer
Correct Option: C
Explanation:

Clear, $\dfrac {1}{8}=0.125, \dfrac {1}{16}=0.0625$ and $\dfrac {1}{25}=0.04$ are terminating decimal fractions.
So, $\dfrac {3}{11}=0.27272727....$ is the non-terminating and repeating decimal.

$4.036$ divided by $0.04$ gives:

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

  1. $1.009$

  2. $10.09$

  3. $100.9$

  4. None of these

Show answer
Correct Option: C
Explanation:

$\dfrac { 4.036 }{ 0.04 } =\dfrac { 403.6 }{ 4 } =100.9$

Divide:
$12.36\div12$

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

  1. $1.3$

  2. $1.03$

  3. $13$

  4. $0.13$

Show answer
Correct Option: B
Explanation:
Multiplying and dividing by $100$ we get
$12.36\div 12 = (1236\div 12)\div100$
                    $=1.03$

Evaluate:
$23.112\div2.4$

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

  1. $9.63$

  2. $96.3$

  3. $9.06$

  4. $963$

Show answer
Correct Option: A
Explanation:
Multiplying and dividing by $100$ we get
$23.112\div 2.4 = (23112\div 24)\div100$
                    $=9.63$

Divide:
$105.55\div 5$

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

  1. $21.11$

  2. $2.111$

  3. $0.211$

  4. $211.1$

Show answer
Correct Option: A
Explanation:
Multiplying and dividing by $100$ we get
$105.55\div 5 = (10555\div 5)\div100$
                    $=21.11$

Evaluate:
$2446.83\div3.1$

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

  1. $244.1$

  2. $789.3$

  3. $78.93$

  4. $7.893$

Show answer
Correct Option: B
Explanation:
Multiplying and dividing by $100$ we get
$2446.83\div 3.1 = (244683\div 31)\div10$
                    $=789.3$