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Multiplying decimals - class-VII

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What is the value of $7.854 \times 10$ ?

  1. $785.4$

  2. $78.54$

  3. $7854$

  4. $78540$


Correct Option: B
Explanation:

$7.854$

  $\times 10$
$\overline{78.540}$

Hence, $7.854 \times 10 = 78.54$

Solve the following:

$0.05 \times 0.09 \times 5 $ 

  1. $0.025$

  2. $0.225$

  3. $0.005$

  4. $0.0225$


Correct Option: D
Explanation:

$0.05 \times 0.09 \times 5$

$=0.05 \times 0.45$
$=0.0225$

$58.326 \times 463.9 \times 0.0081$ is same as 

  1. $5.8326 \times 4.639 \times 8.1$

  2. $5.8326 \times 4.639 \times 0.81$

  3. $58326 \times 4639 \times 0.0000081$

  4. None of these


Correct Option: A
Explanation:

In option A,

$58.326\div10 = 5.8326$
$463.9\div100 = 4.639$
$0.0081\times1000 = 8.1$

Multiplication by $1000$ and Division by $10\times100 = 1000$ gives the same result.

Answer : $5.8326 \times 4.639 \times 8.1$

$5.\overline { 07 } \quad \times 10=y$, then the value of $y$ is

  1. $50.\overline { 07 } $

  2. $50.0\overline { 7 } $

  3. $50.7\overline { 07 } $

  4. $50.70$


Correct Option: C
Explanation:

$5.\overline { 07 } \quad \times 10=50.7070707=50.7\overline { 07 } $

If we write November 8, 1988, as 8.11.88, we see $8\times11=88$. How many such days are in 1972?

  1. 6

  2. 4

  3. 3

  4. 2


Correct Option: A
Explanation:

Multiples of 72 = 2,4,6,8,9,12,18,24,36,72
But in a year we have only 12 months and in a month we have only 30 days
So We have
$24.3.72 = 24\times 3 = 72$
$18.4.72 = 18\times 4 = 72$
$12.6.72= 12\times6 = 72$
$9.8.72 = 9\times8 = 72$
$8.9.72 = 8\times 9 = 72$
$6.12.72 = 6\times 12 = 72$

$\displaystyle 0.04\times 0.08\times 4 $ is equal to

  1. $0.012$

  2. $0.128$

  3. $0.00128$

  4. $0.0128$


Correct Option: D
Explanation:

The rule of thumb in multiplying decimal numbers is we'll count the decimals from the right-hand side and the total places in the decimal in the question will be in the answer.


Example $0.04$ has $2$ places decimal and $0.08$ also has $2$ places. So the total places are $4$. 

The product will have a decimal $4$ places from the right.
$0.04×0.08×4=0.0128$

So option D is the correct answer.

Solve:

$\displaystyle 14.79\times 1000 $ is

  1. $14709$

  2. $14790$

  3. $1479$

  4. $147.9$


Correct Option: B
Explanation:

$14.79\times 1000 = 14790$

Hence Option B

Solve:

$\displaystyle 0.126\times 100 $ is-

  1. $12.6$

  2. $0.126$

  3. $1.26$

  4. $126$


Correct Option: A
Explanation:

$0.126\times100$

$ = (126\times100)/1000$
$=12.6$
Hence Option A

If 0.111 is approximately equal to $\frac {1}{9}$, then the approximate value of 0.777 is

  1. $\frac {5}{9}$

  2. $\frac {7}{9}$

  3. $\frac {2}{9}$

  4. $\frac {1}{9}$


Correct Option: B
Explanation:

$0.777=7\times 0.111$
$=7\times \frac {1}{9}=\frac {7}{9}$

The cost of 1 lit. of milk is Rs. 7.50 then the cost of 30.5 lit. of milk is

  1. Rs. 225.75

  2. Rs. 223.75

  3. Rs. 228.75

  4. none


Correct Option: C
Explanation:

The cost of 1 lit. of milk is Rs. 7.50 .
The cost of 30.5 lit. of milk is 
$\displaystyle 7.50\times 30.5=Rs.228.75$

$0.04\times 0.0162$ is equal to:

  1. $6.48\times { 10 }^{ -3 }$

  2. $6.48\times { 10 }^{ -4 }$

  3. $6.48\times { 10 }^{ -5 }$

  4. $6.48\times { 10 }^{ -6 }$


Correct Option: B
Explanation:

$4\times 162=648$. Sum of decimal places $= 6$.
So, $0.04\times 0.0162=0.000648=6.48\times { 10 }^{ -4 }$

What is $27\times 1.\overline {2} \times 5.526\overline {2} \times 0.\overline {6}$ equal to?

  1. $121.5\overline {7}$

  2. $121.\overline {75}$

  3. $121.7\overline {5}$

  4. None of the above


Correct Option: A
Explanation:

It can be solved as $27\times 1.\overline {2} \times 5.526\overline {2} \times 0.\overline {6}$
$= 27\times \left (1 + \dfrac {2}{9}\right )\times \dfrac {6}{9} \times (5.526\overline {2})$
$= 27\times \dfrac {11}{9}\times \dfrac {2}{3}\times (5.526\overline {2})$
$= 22\times (5.526\overline {2})$
$= 22\times (5.5 + 0.026\overline {2})$
$= 121 + (22\times 0.026\overline {2})$
$= 121 + 0.\overline {57}$
$= 121.\overline {57}$

The value of $\dfrac { 489.1375\times 0.0483\times 1.956 }{ 0.0873\times 92.581\times 99.749 } $ is closest to:

  1. $0.006$

  2. $0.06$

  3. $0.6$

  4. $6$


Correct Option: B
Explanation:

$\dfrac { 489.1375\times 0.0483\times 1.956 }{ 0.0873\times 92.581\times 99.749 } \approx \dfrac { 489\times 0.05\times 2 }{ 0.09\times 93\times 100 } $
$=\dfrac { 489 }{ 9\times 93\times 10 } $
$=\dfrac { 163 }{ 279 } \times \dfrac { 1 }{ 10 } $
$=\dfrac { 0.58 }{ 10 } $
$=0.058\approx 0.06$.

Multiply: $24\times 12.23$

  1. $123.36$

  2. $236.56$

  3. $293.52$

  4. $2935.2$


Correct Option: C
Explanation:
Multiplying and dividing by $100$ we get
$24\times 12.23 = (24\times1223)\div100$
                    $=293.52$

Multiply:
$1563.58\times25$

  1. $39,380.5$

  2. $390.895$

  3. $3,908.95$

  4. $39,089.5$


Correct Option: D
Explanation:
Multiplying and dividing by $100$ we get
$1563.58\times 25 = (156358\times25)\div100$
                    $=39089.5$

Multiply:
$123\times24.53$

  1. $3017.19$

  2. $30171.9$

  3. $307.719$

  4. $30.719$


Correct Option: A
Explanation:
Multiplying and dividing by $100$ we get
$123\times 24.53 = (123\times2453)\div100$
                    $=3017.19$

Solve the following:
$19.7\times 4$


$78.8$

  1. True

  2. False


Correct Option: A
Explanation:

Step 1 : $197 x 4 = 788$

Step 2 : Total number after decimal $= 1$

So, $19.7 \times  4 = 78.8$

Solve the following:
$0.05\times 7$ = $0.35$

  1. True

  2. False


Correct Option: A
Explanation:

Step 1 : $5 \times  7 = 35$

Step 2 : Total number after decimal $= 2$
So, $0.05 \times  7 = 0.35$

Solve the following:
$4.3\times 3.4$


Ans: $14.62$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $4.3 \times  3.4$

Step I: $43 \times 34 = 1462$
Step II: Total number after decimal $= 2$
So, $4.3 \times 3.4 = 14.62$
Hence , given statement is true

Solve the following:
$11.2\times 0.10$


Ans : $1.12$

  1. True

  2. False


Correct Option: A
Explanation:

$11.2 \times  0.10$

Step I: $112 \times  10=1120$

Step II: Total number after decimal point $= 1 + 2 = 3$

So, we put a decimal point after three places from the right

$11.2 \times 0.10 = 1.120$

$= 1.12$


Solve the following:
$0.5\times 0.05$


Ans: $0.025$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $0.5 \times  0.05$


Step I: $5 \times  5 = 25$


Step II: Total number after decimal $= 3$

So, $0.5 \times  0.05 = 0.025$
Hence , given statement is true

Solve the following:
$2\times 0.86$ = $1.72$

  1. True

  2. False


Correct Option: A
Explanation:

$2 \times 0.86 = 1.72$

So given statement is true

Solve the following:
$70.01\times 1.1$


Ans : $77.011$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $70.01 \times  1.1$


Step I: $7001 \times 11 = 77011$


Step II: Total number after decimal $= 3$

So, $70.01 \times 1.1 = 77.011$

Hence , given statement is true

State True/False.
$1.07\times 0.02=0.0214$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $1.07 \times  0.02$


Step I: $107 \times 2 = 214$


Step II: Total number after decimal = 4


So, $1.07 \times 0.02 = 0.0214$

Hence , given statement is true

State True/False.
$10.05\times 1.05=10.5525$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $10.05 \times  1.05$


Step I: $1005 \times  105 = 105525$

Step II: Total number after decimal $= 4$

So, $10.05 \times  1.05= 10.5525$

Hence , given statement is true

Solve the following:
$101.01\times 0.01$ 


Ans : $1.0101$

  1. True

  2. False


Correct Option: A
Explanation:

Given, $101.01 \times 0.01$


Step I: $10101 \times  001 = 10101$


Step II: Total number after decimal $= 4$

So, $101.01 \times 0.01 = 1.0101$

Hence , given statement is true

What is the missing value in the given mathematical statement?
$0.25\times 12 = 0.25 \times 3 + 0.25 \times 3 + 0.25\times$ ________.

  1. $2$

  2. $3$

  3. $6$

  4. $8$


Correct Option: C
Explanation:

Using distributive property, we have
$0.25\times 12 = 0.25 \times (3 + 3 + 6)$
$\Rightarrow 0.25\times 12 = 0.25 \times 3 + 0.25\times 3 + 0.25 \times 6$.

$5.25\times 9.1\times 0.0\times 8.26=$ ____________.

  1. $47.775$

  2. $0.1176$

  3. $0$

  4. $1$


Correct Option: C
Explanation:

The value of $5.25\times 9.1\times 0.0\times 8.26$ is

$(47.775)\times (0)$
$=0$

The value of $\dfrac{0.008\times 0.01\times 0.0072}{(0.12\times 0.0004)}$ is:

  1. $0.012$

  2. $0.12$

  3. $1.02$

  4. $1.2$


Correct Option: A
Explanation:

Given expression 


$\dfrac{0.008\times 0.01\times 0.0072}{(0.12\times 0.0004)}$ 

$=\dfrac {0.008\times0.01\times0.0072}{0.000048}$

$=0.00008\times\dfrac{0.0072}{0.000048}$

$=\dfrac{8}{48}\times\dfrac{72}{1000}$

$=0.012$

Find the value of following expression:
$\dfrac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$

  1. $2$

  2. $2.40$

  3. $2.43$

  4. $2.50$

  5. $None\ of\ these$


Correct Option: A

Number of zero's in the product of
$5 \times 10 \times 25 \times 40 \times 50 \times 55 \times 65 \times 125 \times 80 $

  1. $8$

  2. $9$

  3. $12$

  4. $13$


Correct Option: B
Explanation:

$5 \times 10 \times 25 \times 40 \times 50 \times 55 \times 65 \times 125 \times 80 $
$= 5 \times 2 \times 5 \times 5^2 \times 2^3 \times 5 \times 2 \times 5^2 \times 11 \times 5 \times 13 \times 5 \times 5^3 \times 2^4 \times 5$
$= 2^9 \times 5^{13}\times 11 \times 13 = (2 \times 5)^9 \times 5^4 \times 11 \times 13$


As we know that zeroes are formed by the product of a $2$ and a $5$ i.e. $2$ x $5$. 

Therefore, number of zeroes depends on the number of pairs of $2$'s and $5$'s that can be formed in the given product. 

Since $9$ pairs of $2$'s and $5$'s are formed in the given product, hence there will be $9$ zeroes in the given product.

If u, v and w are the digits of decimal system, then the rational number represented by 0.uwuvuvuvuv......is

  1. (100 uw + 99 uv)/99

  2. (99uw + uv)/980

  3. (99uw + uv)/9900

  4. (9uw + 99uv)/900


Correct Option: C
Explanation:

x =0.uwuvuvuvuv...
x = O.uwuv
(i) x 100
100x = uw. uv
(ii) x 100
10000x = uwuv - uv
(iii) - (ii)

Each piece of cardboard is $0.3\ cm$ thick. If Marie stacks $8$ pieces of cardboard on top of one another, how thick will the stack be?

  1. $2.4\ cm$

  2. $24\ cm$

  3. $2.1\ cm$

  4. $21\ cm$


Correct Option: A
Explanation:

It is given that each piece of cardboard is $0.3$ cm thick which means that one piece is $0.3$ cm thick.


If Marie stacks $8$ pieces of cardboard, then the thickness of $8$ pieces of cardboard will be:

$0.3\times 8=2.4$ cm

Hence, the stack will be $2.4$ cm thick.

If $100\times \text{ ? }=352$. Then, find the missing number.

  1. $0.352$

  2. $352$

  3. $35.2$

  4. $3.52$


Correct Option: D
Explanation:

Let $x$ be the missing number.


$100\times x=352\ \Rightarrow 100x=352\ \Rightarrow x=\dfrac { 352 }{ 100 } \ \Rightarrow x=352\times 0.01\quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow x=3.52$

Hence, the missing number is $3.52$.

Calculate $456.78\times 8$.

  1. $36542.4$

  2. $365.424$

  3. $3,654.24$

  4. $36.5424$


Correct Option: C
Explanation:
Let us first multiply the two given numbers $456.78$ and $8$ without decimal point:

$45678\times 8=365424$

Since, $456.78$ has two decimal places, therefore the answer $365424$ should also have two decimal places that is $3654.24$.

Hence, $456.78\times 8=3,654.24$.

$45.678\times \text{ ? }=1187.628$. Find $?$.

  1. $26$

  2. $27$

  3. $28$

  4. $29$


Correct Option: A
Explanation:

Let $x$ be the missing number.


$45.678\times x=1187.628\ \Rightarrow 45.678x=1187.628\ \Rightarrow \dfrac { 45678x }{ 1000 } =\dfrac { 1187628 }{ 1000 } \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow x=\dfrac { 1187628 }{ 1000 } \times \dfrac { 1000 }{ 45678 } \ \Rightarrow x=26$

Hence, the missing number is $26$.

Multiply $43.09$ with $23$.

  1. $99.107$

  2. $991.07$

  3. $9910.7$

  4. $9.9107$


Correct Option: B
Explanation:
Let us first multiply the two given numbers $43.09$ and $23$ without decimal point:
$4309\times 23=99107$
Since, $43.09$ has two decimal places, therefore the answer $99107$ should also have two decimal places that is $991.07$.
Hence, $43.09\times 23=991.07$.

(Three rupees $5$ paise) $\times$ (five rupees $40$ paise) is equal to

  1. $Rs. 18.90$

  2. $Rs. 16.47$

  3. $Rs. 17.64$

  4. $RS. 15.37$


Correct Option: B
Explanation:

We know that 100 paise is nothing but 1 Rupee.

So $5Paise =  0.05 Rupees$
Also $40 Paise = 0.4 Rupees$
Now Three Rupees $5 Paise = 3 Rupees + 0.05 Rupees$
                                               $=3.05 Rupees$
Also Five Rupees $40 Paise= 5 Rupees + 0.40 Rupees$
                                              $= 5.40 Rupees$
Now to find $(Three\quad rupees\quad 5paise)×(fiverupees\quad 40paise)$
$3.05\times 5.40 = 16.47$

Solve the following:
$210.01\times 5$ = $1050.05$

  1. True

  2. False


Correct Option: A
Explanation:

Step 1 : $21001 x 5 = 105005$

Step 2 : Total number after decimal $= 2$
So, $210.01 \times  5 = 1050.05$

Using  identity the value obtained from the product $25.4 \times 24.6$ is

  1. $624.84$

  2. $642.84$

  3. $264.84$

  4. $62.84$


Correct Option: A
Explanation:


Given

$25.4\times24.6$

we can re-wright them as

$(25+0.4)\times (25-0.4)$

$\because \ we \ have \ an\ identity \ (a+b) (a-b)=a^2-b^2$

$a=25,\ b=0.4$


$= (25)^2-(0.4)^2$

$= 625- 0.16$

$=624.84$

$\therefore option\ A\ is\ correct.$


Without actual multiplication, the value $79.01 \times 79.01 + 2 \times 79.01 \times 20.99 + 20.99 \times 20.99$

  1. $10,009$

  2. $1000.06$

  3. $10,000$

  4. $1007$


Correct Option: C
Explanation:
$79.01\times 79.01+2\times 79.01\times 20.99+20.99\times 20.99....(1)$
$\dfrac {7901}{100}\times \dfrac {7901}{100}+2\times \dfrac {7901}{100}\times  \dfrac {2099}{100}+\dfrac {2099}{100}\times \dfrac {2099}{100}....(2)$

$7901\times 7901=(7901)^2 =(7900 +1)^2$    $\quad [\because \ 79^2=(80-1)^2\\ =80^2+1-2.80\\ =6400+1-160\\ =6241]$
$=(7900)^2 +1^2+2(7900)(1)$
$=62410000+1+15800$
$=62425801$ 

$2099\times 2099 =(2099)^2=(2100-1)^2$ $\quad [\because \ 21^2=(20+1)^2\\ =20^2+1+2.20\\ =400+40+1\\ =441]$
$=(2100)^2+1^2-2(2100)(1)$
$=4410000+1-4200$
$=4405801$

$7901\times 2099=(7900+1) (2100-1)$
$=(7900)(2100)-7900+2100-1$
$=16590000-7900+2100-1$
$=16584299\ =16584199$
from $(2)$
$\dfrac {62425801}{10000}+\dfrac {2\times 16584199}{10000}+\dfrac {4405801}{10000}$
$6242.5801+\dfrac {33168398}{10000}+440.5801$
$6242.5801+3316.8398+440.5801$
$=10,000$

Product of $78.12$ and $1.5$ is :

  1. $117.81$

  2. $117.18$

  3. $117.32$

  4. $117.80$


Correct Option: B
Explanation:

The product of $78.12$ and $1.5$ is

 $78.12 \times 1.5=117.18$
Hence, the answer is $117.18$.

Product of $\displaystyle 3.92\times 0.1\times 0.0\times 6.3$ is:

  1. $0.392$

  2. $0.1176$

  3. $0$

  4. $6.3$


Correct Option: C
Explanation:

We know if we multiply $0$ by any number then result will be zero.

So the value of $ 3.92\times .01\times 0.0\times 6.3=0$
Hence, the answer is $0$.

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