Decimal Operations and Arithmetic - Class VII

 $617.00$
     $6.017$
     $0.617$
$+$ $6.0017$
-----------------
  $629.6357$
-----------------

Addition of $3.005$ and $4.7$ gives $3.005+4.7=7.705$

The sum of $1.2$ and $2.3$ will be $1.2+2.3=3.5$

$2.\bar{3}-0.\bar{4}=1.\bar{9}$

$\Rightarrow$  $0.\overline {23}$ means $0.232323....$

    $0.7500$
$-   0.0075$

    $0.7425$

$\therefore$  Required difference $= 0.7425$.

$x = 301.01 - 0.101 - 198.01$
   $= 301.01 - 198.111 = 102.899$

$\displaystyle\frac { 10.24 }{ 1.6 } = \displaystyle\frac { 102.4 }{ 16 } = 6.4$
$\therefore \displaystyle\frac { 10.24\div 1.6 }{ 20-19.8 } = \displaystyle\frac { 6.4 }{ 0.2 } = \displaystyle\frac { 64 }{ 2 } = 32$

$\displaystyle \left [ 0.9-\left { 2.3-3.2-\left ( 7.1-5.4-3.5 \right ) \right } \right ]$

$\displaystyle 0.34\overline{67}+0.13\overline{33}=\frac{3467-34}{9900}+\frac{1333-13}{9900}$

$\displaystyle 6\frac{1}{4}\times 0.25+0.75-0.3125$
$= 6.25 \times 0.25 + 0.75 - 0.3125$
$= 1.5625 + 0.75 - 0.3125$
$= 2.3125 - 0.3125 = 2$

$\displaystyle 0.\overline{2}+0.\overline{3}+0.\overline{4}+0.\overline{9}+0.\overline{39}$

$\displaystyle :0.\overline{4}+0.\overline{61}+0.\overline{11}-0.\overline{36}=\frac{4}{9}+\frac{61}{99}+\frac{11}{99}-\frac{36}{99}=\frac{4}{9}+\frac{72}{99}-\frac{36}{99}$

32.000-27.091=4.909

For obtaining the sum of decimal numbers with different decimal values we expand the decimal values of all the numbers with respect to the number with the highest decimal value. 

$\frac {0.1}{0.01}+\frac {0.01}{0.1}=10+\frac {1}{10}$
$=10+0.1$
$=10.1$

To add $3$ decimal numbers of different decimal values we pick the number with the highest decimal value and expand all the other numbers to the same value by adding $0$ after the decimal point.

The sum of two numbers $=31.021$

$5 + \dfrac { 3}{100} + \dfrac{4}{1000}$

$\displaystyle \frac{0.1}{0.01}+\frac{0.01}{0.1}=10+\frac{1}{10}$
=10+0.1
=10.1

As given,

Let $3889 + 12.952 - x = 3854.002$.
Then $x=\left( 3889+12.952 \right) -3854.002$
             $= 3901.952 - 3854.002$
             $= 47.95$.

The value of $2.\overline {6} - 1.\overline {9}$ is
$= \left (2 + \dfrac {6}{9}\right ) - \left (1 + \dfrac {9}{9}\right )$
$= \dfrac {6}{9} = 0.\overline {6}$

$3.\overline { 87 } -2.\overline { 59 } =\left( 3+0.\overline { 87 }  \right) -\left( 2+0.\overline { 59 }  \right) $

We have, $(30.5 - 30.4) + (30.3 - 30.2) + (30.1 - 30) + (29.9 - 29.8) + (29.7 - 29.6) + (29.5 - 29.4) + (29.3 - 29.2) + (29.1 - 29.0)$
$= 0.1+ 0.1 + 0.1 + 0.1 + 0.1+ 0.1 + 0.1 + 0.1$
$= 0.8$.

The sum of $11.006+34+0.72$ is $45.726$.
Now, the number $45.726$ is rounded off as $45.73$.

given that, $617.0000+6.0170+0.6170+6.0017=629.6357$

$5.5-4.17=1.33$

${\left( 1.02 \right)}^{4} + {\left( 0.98 \right)}^{4}$

Width of class $=U.L-L.L=60.5-55.5=5$

The weight of the water alone is 150.35g - 64.27g = 86.08g. If the flask is 0.75 times full, the water weighs 0.75 * 86.08g = 64.56g. Adding the empty flask weight (64.27g) gives 128.83g.

The given expression is

$2.002+7.9\left{ 2.8-6.3\left( 3.6-1.5 \right) +15.6 \right} $
$=2.002+7.9\left{ 2.8-6.3\times 2.1+15.6 \right} $
$=2.002+7.9\left{ 2.8-13.23+15.6 \right} $
$=2.002+7.9\left{ 5.17 \right} $
$=2.002+40.843=42.845$

The value of $25 $ $+$ $\displaystyle{\frac{3}{100}}$ $+$ $\displaystyle{\frac{4}{1000}}$ is

$\displaystyle{\frac{0.1}{0.01} + \frac{0.01}{0.1}}$ = 10 + $\displaystyle{\frac{1}{10}}$ $= 10 + 0.1 = 10.1$

3 tens 6 thousandths is

The expression is 58 + 0.03 + 0.007. Adding these values together results in 58.037.

$\displaystyle{\frac{280.5}{25.5}}$ = $\displaystyle{\frac{280.5}{25.5} \times \frac{10}{10} \times \frac{10}{10} = \frac{2805}{2.55} \times \frac{1}{100} = \frac{1100}{100}}$ = 11

$\displaystyle \frac{0.34-0.034}{0.0034\div 34}=\frac{0.306}{0.0001}=\frac{0.3060}{0.0001}$

Given, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49}$

Using the identity $a^2 - b^2 = (a+b)(a-b)$
$\therefore \displaystyle 0.25\times 0.25 - 0.24\times 0.24 = (0.25+0.24)(0.252-0.24) = (0.49)(0.01)$

Thus, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49} = \frac {0.49\times 0.01}{0.49}$ = $0.01$

$\displaystyle \frac{42.31-26.43}{42.31+26.43}\div \frac{423.1-264.3}{4.231+2.643}$

Let us first write the mixed fraction $2\dfrac {3}{10}$ in decimals as follows:

We solve the given expression as follows:

$\displaystyle 3.\overline{36}-2.\overline{05}+1.\overline{33}$

$515.15-15.51-1.51-5.11-1.11.$

Given expression:

(I) $715+12.59+685.35=1412.94$
(II) $518-(216.80-115.96)=518-100.84=417.16$
(III) $4.090+0.050+6.500=10.640$
(IV) $36.050+198.05-21.03=213.07$.

from question 

$3.7-1.9$

The sum of $0.5 ,12.56$ and $0.003$ is

Total number of members in family $\rightarrow$ $5$