Decimal Operations - Class VII

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

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

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

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

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

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

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

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

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

correct option is C..

$122.5/1000$

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

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. 

$150.75\div 0.6$

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

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

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

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.

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

Given, $127.1\div 1000$

Given, $0.45\div 5$

Given, $0.4\div 20$

Given, $44.3\div 10$

Given, $23\div 100$

To solve 0.99x = 100, divide 100 by 0.99. This is equivalent to 10000/99, which equals 101.010101...

$54.327 \times 357.2 \times 0.0057 = \cfrac {54327}{1000} \times \cfrac {3572}{10} \times \cfrac {57}{10000}$

We will first convert the decimals into fraction in the given fraction and then solve it as follows:

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. 

$\sqrt{0.4\times 0.04\times a}=0.004\times 0.4\times \sqrt{b}$ 

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) $
                             $= 0.86$

We know that in general, $\dfrac {1}{10}=0.1$.

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:

As we know $1$ Rs $= 100$ paisa

Division of $125.625$ by $0.5$ is