Tag: calculating and mental strategies 3

Questions Related to calculating and mental strategies 3

Evaluate: $25.25\div2.5$

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

  1. $1.001$

  2. $11$

  3. $1.1$

  4. $10.1$

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Correct Option: D
Explanation:
Multiplying and dividing by $10$ we get
$25.25\div 2.5 = (2525\div 25)\div10$
                    $=10.1$

Solve the following:

$127.1÷1000$

Ans : $0.1271$

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

  1. True

  2. False

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Correct Option: A
Explanation:

Given, $127.1\div 1000$


Could be written as,


$= \dfrac{1271}{10}\times \dfrac{1}{1000}$

$= \dfrac{1271}{10000}$

$= 0.1271$

So, given statement is true.

Solve the following:
$0.45\div 5$


Ans: $0.09$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given, $0.45\div 5$


Could be written as,


$= \dfrac{45}{100}\times \frac{1}{5}$

$= \dfrac{9}{100}$

$= 0.09$

So, given statement is true.

Solve the following:
$0.4\div 20$


Ans: $0.02$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Given, $0.4\div 20$


Could be written as,


$= \dfrac{4}{10}\times \dfrac{1}{20}$

$= \dfrac{2}{100}$

$= 0.02$
So, given statement is true.

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. $11.\overline{01}$

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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,

$999x=621$

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

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