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Calculating and mental strategies 3 - class-VII

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Express as rupees using decimals,

  1. $5\ paise$

  2. $75\ paise$

  3. $20\ paise$

  4. $50\ rupees\ 90\ paise$


Correct Option: A
Explanation:
let $1paisa$ =$100 rs$
So,
$(i).$
$=>5paisa=\dfrac{5}{100}=0.005rs$

$(ii).$

$=>75paisa=\dfrac{75}{100}=\dfrac{3}{4}=0.75rs$

$(iii).$
$20paisa=\dfrac{20}{100}=0.2rs$

$(iv).$

$50rs$ $90paisa=50rs+90paisa$

$=>50+\dfrac{90}{100}$

$>=50+0.9=50.9rs$


























Find the value of $x$: $10.5 \div x = 1.05 \div 0.5$.

  1. $0.05$

  2. $105$

  3. $0.105$

  4. $5$


Correct Option: D
Explanation:

$\displaystyle\frac { 10.5 }{ x } = \displaystyle\frac { 1.05 }{ 0.5 } $

$x = \displaystyle\frac { 10.5\times 0.5 }{ 1.05 } = \displaystyle\frac { 105\times 5 }{ 105 } = 5$

If $\displaystyle\frac { 1 }{ 6.198 } = 0.16134$, then the value of $\displaystyle\frac { 1 }{ 0.0006198 } $ is.

  1. $16134$

  2. $1613.4$

  3. $0.16134$

  4. $0.016134$


Correct Option: B
Explanation:

$\displaystyle\frac { 1 }{ 0.0006198 } = \displaystyle\frac { 1 }{ \displaystyle\frac { 6.198 }{ 10000 }  } = \displaystyle\frac { 10000 }{ 6.198 } $

$= 10000 \times 0.16134 = 1613.4$

Consider the following quotients:
I.   $368.39$ divided by $17$.
II.  $170.50$ divided by $62$.
III. $875.65$ divided by $83$.
Their correct sequence in decreasing order is ?

  1. I, III, II

  2. II, I, III

  3. II, III, I

  4. III, I, II


Correct Option: A
Explanation:

(I) $\displaystyle\frac{368.39}{17} = 21.67$


(II) $\displaystyle\frac{170.50}{62} = 2.75$

(III) $\displaystyle\frac{875.65}{83} = 10.55$

$\therefore$ The correct sequence in decreasing order is (I), (III), (II).

Simplified value for $(17.5+2.5)\div 5$ is

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: D
Explanation:

$\left( 17.5+2.5 \right) \div 5$

$=\left( 20.0 \right) \div 5$
$ =20\div 5$

$ =4$
So, correct answer is option D.

If $\displaystyle \frac{547.527}{0.0082}=x $, then the value of $\displaystyle \frac{547527}{82}$ is 

  1. $\displaystyle \frac{x}{10}$

  2. 10x

  3. 100x

  4. $\displaystyle \frac{x}{100}$


Correct Option: A
Explanation:

Given, $\displaystyle \frac{547.527}{0.0082}=x $


$\displaystyle \Rightarrow \frac{5475270}{82}=x $

$\displaystyle \Rightarrow \frac{5475270}{82}=\frac{x}{10} $

The sum of first 100 natural numbers is divisible by

  1. $10$

  2. $100$

  3. $50$

  4. All the above


Correct Option: D
Explanation:

The sum of the $n$ natural numbers =$\frac{n\times (n+1)}{2}$
Here,$n=100$
$\therefore$ Sum=$\frac{100\times (100+1)}{2}$
$=\frac{100\times 101}{2}$
$=5050$
Option is D

How many numbers from 1 to 100 written in decimal form have the digit 5 in them?

  1. $11$

  2. $10$

  3. $15$

  4. $19$


Correct Option: D
Explanation:

The numbers can be easily counted.
5,15,25,35,45,50,51,52,53,54,55,56,57,58.59.65.75.85.95
Thus, there are 19 numbers

The number equal to 7 hundredths is

  1. 0.7

  2. 0.07

  3. 0.007

  4. 1.07


Correct Option: B
Explanation:

$\frac{7}{100} = 0.07$

The number equal to 22 thousandths is

  1. 0.22

  2. 0.022

  3. 2.022

  4. 2.202


Correct Option: B
Explanation:

$\frac{22}{1000} = 0.022$

$\displaystyle 225.500\div 0.5$ =

  1. 4.51

  2. 45.1

  3. 451

  4. .451


Correct Option: C
Explanation:

correct option is C..

Solve:
$\displaystyle 122.5 \div 1000 = $

  1. $.01225$

  2. $.1225$

  3. $1.225$

  4. $12.25$


Correct Option: B
Explanation:

$122.5/1000$

$=1225/10000$
$=0.1225$
Hence Option B

If the cost of $20$ fans is Rs. $248.50$, then the cost of one fan is

  1. $Rs.\ 12.46$

  2. $Rs.\ 12.42$

  3. $Rs.\ 12.40$

  4. $Rs.\ 12.425$


Correct Option: D
Explanation:

cost of $20$ fans = Rs. $248.50$

cost of $1$ fan = Rs. $248.50/20$=$12.425$ Rs.
Hence Option D

3 tenth 5 thousandths is written as

  1. 35.00

  2. 0.35

  3. 3.5

  4. 0.305


Correct Option: D
Explanation:

The first decimal digit from the decimal point is the tenth, the second decimal digit from the decimal point is the hundredth and the third decimal digit from the decimal point is the thousandths digit. 


Read the whole set of three decimal digits as a number, and say, "tenths", "hundredths" and “thousandths.” 0.305 has 3 tenths, 0 hundredths, and 5 thousandths. While 0.305 is the sum of 3/10, 0/100, and 5/1000, it is also 305/1000.

So option D is the correct answer.

Divide $150.75\div 0.6$

  1. 251.25

  2. 2512.5

  3. 25125

  4. 25.125


Correct Option: A
Explanation:

$150.75\div 0.6$

$\Rightarrow$  $\dfrac{150.75}{0.6}=\dfrac{150.75\times 10}{0.6\times 10}$

                     $=\dfrac{1507.5}{6}$

                     $=251.25$

$143.6\div 2000= .............$

  1. 0.1718

  2. 7.18

  3. 0.718

  4. 0.0718


Correct Option: D
Explanation:

$143.6\div 2000=71.8\div 1000$
$=0.0718$

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

  1. 58.0037

  2. 58.37

  3. 58.037

  4. none of these


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) $

  1. 0

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

  3. 1.2

  4. 10

  5. 12


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

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

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

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

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

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


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:

  1. $1.009$

  2. $10.09$

  3. $100.9$

  4. None of these


Correct Option: C
Explanation:

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

Divide:
$12.36\div12$

  1. $1.3$

  2. $1.03$

  3. $13$

  4. $0.13$


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

Evaluate:
$23.112\div2.4$

  1. $9.63$

  2. $96.3$

  3. $9.06$

  4. $963$


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

Divide:
$105.55\div 5$

  1. $21.11$

  2. $2.111$

  3. $0.211$

  4. $211.1$


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

Evaluate:
$2446.83\div3.1$

  1. $244.1$

  2. $789.3$

  3. $78.93$

  4. $7.893$


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

Evaluate: $25.25\div2.5$

  1. $1.001$

  2. $11$

  3. $1.1$

  4. $10.1$


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 : $0.1271$

  1. True

  2. False


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: $0.09$

  1. True

  2. False


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: $0.02$

  1. True

  2. False


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 : $4.43$

  1. True

  2. False


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 : $0.023$

  1. True

  2. False


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 $\left(\displaystyle\frac{0.1}{0.01}+\frac{0.01}{0.1}\right)$?

  1. $10.1$

  2. $1.10$

  3. $1.01$

  4. $10.0$


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 = ?

  1. $101.01$

  2. $11.01$

  3. $101. \overline{01}$

  4. $11.\overline{01}$


Correct Option: A

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

$0.\overline{37}$

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

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

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

  4. None of the above


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 $\dfrac{p}{q}$: 

$0.\overline{621}$

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

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

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

  4. None of the above


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

  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. $5432.7\times 3.572\times 0.000057$


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 ? 

  1. $1$ metre

  2. $1.5$ metres

  3. $15.0$ metres

  4. $0.15$ metres


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

  1. $0.2$

  2. $0.3$

  3. $0.6$

  4. $0.8$


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?

  1. (-1,-2)

  2. (-3,-4)

  3. (-2,-3)

  4. (-4,-5)


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 

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

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

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

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


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:

  1. $0.86$

  2. $0.95$

  3. $0.97$

  4. $1.06$


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} = $

  1. $162.357$

  2. $1.62357$

  3. $16.2357$

  4. $0.162357$


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)

  1. left, $2$

  2. right. $3$

  3. left, $3$

  4. right. $2$


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:
$1234.46\div8$

  1. $15430.75$

  2. $15403.075$

  3. $154.3075$

  4. $15.43075$


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._____

  1. $4.25$

  2. $42.5$

  3. $4.5$

  4. $2.5$


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.

  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. $5432.7\times 3.572\times 0.000057$


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

  1. $1.331$

  2. $1.221$

  3. $1.484$

  4. $1.551$


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 $0.5$

  1. $251.25$

  2. $2512.5$

  3. $25125$

  4. $25.125$


Correct Option: A
Explanation:

Division of $125.625$ by $0.5$ is

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

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