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Decimal Fraction
1.
$\text{Evalute}:\frac{{\left(2.39\right)}^{2}-{\left(1.61\right)}^{2}}{2.39-1.61}$

Explanation:

Solution:
$\begin{array}{rl}& \text{Given}\phantom{\rule{thinmathspace}{0ex}}\text{Expression}=\\ & \frac{{a}^{2}-{b}^{2}}{a-b}=\frac{\left(a+b\right)\left(a-b\right)}{\left(a-b\right)}\\ & =\left(a+b\right)=\left(2.39+1.61\right)=4\end{array}$

2.What decimal of an hour is a second ?

Explanation:

Solution:
$\begin{array}{rl}& \text{Required}\phantom{\rule{thinmathspace}{0ex}}\text{decimal}=\\ & \frac{1}{60×60}=\frac{1}{3600}=.00027\end{array}$

3.
$\text{The}\phantom{\rule{thinmathspace}{0ex}}\text{value}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\frac{{\left(0.96\right)}^{3}-{\left(0.1\right)}^{3}}{{\left(0.96\right)}^{2}+0.096+{\left(0.1\right)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\text{is}:$

Explanation:

Solution:
$\begin{array}{rl}& \text{Given}\phantom{\rule{thinmathspace}{0ex}}\text{expression}\\ & =\frac{{\left(0.96\right)}^{3}-{\left(0.1\right)}^{3}}{{\left(0.96\right)}^{2}+\left(0.96×0.1\right)+{\left(0.1\right)}^{2}}\\ & =\left(\frac{{a}^{3}-{b}^{3}}{{a}^{2}+ab+{b}^{2}}\right)\\ & =\left(a-b\right)\\ & =\left(0.96-0.1\right)\\ & =0.86\end{array}$

4.If 2994 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

Explanation:

Solution:
$\begin{array}{rl}& \frac{29.94}{1.45}=\frac{299.4}{14.5}\\ & =\left(\frac{2994}{14.5}×\frac{1}{10}\right)\phantom{\rule{thinmathspace}{0ex}}\left[\text{Here,}\phantom{\rule{thinmathspace}{0ex}}\text{Substitute}\phantom{\rule{thinmathspace}{0ex}}172\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{place}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\frac{2994}{14.5}\right]\\ & =\frac{172}{10}\\ & =17.2\end{array}$

5.When 0.232323..... is converted into a fraction, then the result is:

Explanation:

Solution:
$0.232323...=0.\overline{23}=\frac{23}{99}$

6.
$\frac{.009}{?}=.01$

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\frac{.009}{x}=.01;\\ & \text{Then}\phantom{\rule{thinmathspace}{0ex}}x=\frac{.009}{.01}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\frac{.9}{1}\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=.9\end{array}$

7.The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:

Explanation:

Solution:
Given expression = (11.98)2 + (0.02)2 + 11.98 x x.
For the given expression to be a perfect square, we must have
11.98 x x = 2 x 11.98 x 0.02 or x = 0.04

8.3889 + 12.952 - ? = 3854.002

Explanation:

Solution:
Let 3889 + 12.952 - x = 3854.002.
Then x = (3889 + 12.952) - 3854.002
= 3901.952 - 3854.002
= 47.95.

9.0.04 x 0.0162 is equal to:

Explanation:

Solution:
4 x 162 = 648. Sum of decimal places = 6.
So, 0.04 x 0.0162 = 0.000648 = 6.48 x 10-4

10.
$\begin{array}{rl}& \frac{4.2×4.2-1.9×1.9}{2.3×6.1}\phantom{\rule{thinmathspace}{0ex}}\\ & \text{is}\phantom{\rule{thinmathspace}{0ex}}\text{equal}\phantom{\rule{thinmathspace}{0ex}}\text{to:}\end{array}$

$\begin{array}{rl}& Given\phantom{\rule{thinmathspace}{0ex}}Expression\\ & =\frac{\left({a}^{2}-{b}^{2}\right)}{\left(a+b\right)\left(a-b\right)}\\ & =\frac{\left({a}^{2}-{b}^{2}\right)}{\left({a}^{2}-{b}^{2}\right)}\\ & =1\end{array}$