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the number 1.45450450450450450450450450...... how can be written as an ordinary fraction ?

$$\\ \small{\text{
I.
$
1.45450450450450450450450450\dots = 1.4545 + 0.0000\overline{045} = \frac{14545} {10000} + 0.0000\overline{045} =\frac{2909}{2000} + 0.0000\overline{045}
$
}}$\\\\$
\small{\text{
II.
$
0.0000\overline{045} = 045*10^{-7} + 045*10^{-10} + 045*10^{-13} + 045*10^{-16} + \dots
$
}}
$\\$
\small{\text{
$
0.0000\overline{045} = (\underbrace{045*10^{-7}}_{=a}) + (045*10^{-7}) *10^{-3} + (045*10^{-7})*10^{-6} + (045*10^{-7})*10^{-9} + \dots
$
\textcolor[rgb]{1,0,0}{ this is a geometric series. }
}}
$\\$
\small{\text{
The sum of the geometric series is $ s=\frac{a}{1-r}$ we have $a=045*10^{-7}$ and $ r = \frac{ (045*10^{-7}) *10^{-3} }{ 045*10^{-7} } = \frac{ (045*10^{-7})*10^{-6} }{ (045*10^{-7}) *10^{-3} } = ... = 10^{-3}
$
}}
$\\$
\small{\text{
$
\begin{array}{rcl}
s &=& \frac{ 045*10^{-7} }{ 1- 10^{-3} } \\ \\
&=& \frac{10^3}{10^3}*\frac{ 045*10^{-7} }{ 1- 10^{-3} } \\\\
&=& \frac{45}{10^4(10^3-1)} \\\\
&=& \frac{45}{ 9990000 }
\end{Array}
$
}}$\\\\$
\small{\text{
III.
$
1.45450450450450450450450450\dots = 1.4545 + 0.0000\overline{045} = \frac{14545} {10000} + 0.0000\overline{045} =\frac{2909}{2000} + \frac{45}{ 9990000 }
$
}}$\\\\$
\small{\text{
$
1.45450450450450450450450450\dots
= \frac{2909}{2000} + \frac{45}{ 9990000 }
= \frac{2909}{2000} + \frac{1}{ 2220000 }
= \frac{3229}{2220}
$
}}$$

if 5% is 14.8

then

100% is x

x=(100*14.8)/5

x=$${\frac{\left({\mathtt{100}}{\mathtt{\,\times\,}}{\mathtt{14.8}}\right)}{{\mathtt{5}}}} = {\mathtt{296}}$$

Here's another way to figure this without using much math....

100% is 20 times 5%

So....what is 20 times $14.80.....???

If 5% is 14.80 then

1% would be 14.80/5

and

100% must be  100*14.80/5         

It is y=sqrt(x)

If the square root is written into the question then the answer is positive.  [this is  the convention]

See the graph.

Mmm that's a tough one ???   I assume you replace each question mark with just one number or symbol?

I seem to do this a little differently from everybody else on here

Forget the whole number part for a moment

Write the non-repeating part and the repeating part of the decimal = 45450

Subtract the non-repeating part from this....=  [45450 - 45  ] = 45405

Put this number over a fraction consisting of 9's and 0's.....the number of leading 9's  equaling the number of digits in the repeating part (3), and the number of trailing 0's equaling the number of digits in the non-repating part (2)..so we have

45405 / 99900 = 1009 / 2220

Add back the  whole number part.....so we have

1 + 1009/2220  = [2220 + 1009] / 2220 = 3229/2220   ...verify for yourself that this is the same as what we started with...!!!

My answer and Melody's are approximately the same -  depending on the level of rounding. She has taken a "ratio" approach, while I have have used a "trig" approach.......same dog, different fleas....

And heureka has provided a very nice LaTex answer....utilizing a combination of both things....!!!

Tan Theta = -8/15, Pi/2<Theta<pi

First this is the second quad so 

sin and cosec are positive and the rest will be negative.

Now you don't need to worry about again until the end.

Finsd the length of the hypotenuse using pythagoras's theorum

then read the ratios straight of the triangle and assign the appropriate signs.    

A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius

arc length  b = 5.92 m

angle  $$\alpha \ensurement{^{\circ}}$$ = $$107.9\ensurement{^{\circ}}$$

radius r = ?

$$\boxed{b =r* \breve \alpha} \qquad \breve \alpha =\alpha \ensurement{^{\circ}} * \frac{2\pi}{360\ensurement{^{\circ}}} = \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}} \\\\
\begin{array}{rcl}
b &=& r* \breve \alpha \\
&=& r * \alpha \ensurement{^{\circ}} *\frac{\pi}{180\ensurement{^{\circ}}}
\end{array}\\\\\\
\boxed{r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{b} {\alpha\ensurement{^{\circ}}} = 57.2957795131*\frac{b} {\alpha\ensurement{^{\circ}}} }\\\\
\small{\text{
$
r = \left( \frac{180\ensurement{^{\circ}} }{\pi} \right)*\frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 57.2957795131 * \frac{5.92\ m}{107.9\ensurement{^{\circ}}} = 3.14356825503\ m
$
}}$$

Radius is 3.14356825503 m

A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius

Let us convert 107.9 degrees to radians = 107.9 x pi / 180 = about 1.883 rads

And using  S = rΘ   where S= the arc length and Θ is in radians, we have

5.92m = r (1.883)     divide both sides by (1.883)

r = about 3.144m

A sector has an angle of 107.9 and an arc length of 5.92m. Find its radius

There are 360 degrees in a circle so we hve 107.9/360  of the circle here.

$$\\P=\frac{ 107.9}{360} *2\pi *r\\\\
5.92=\frac{ 107.9}{360} *2\pi *r\\\\
r=\frac{5.92*360}{(107.9*2*\pi)}\\\\$$

$$2.78 \times 10^{-10}
=00000000000000000002.78\times 10^{-10}$$

Now move the decimal point 10 places in the direction to make the number smaller.   

$$\\-1-(-5x)-2x+2x^2+7\\
=-1--5x-2x+2x^2+7\\
=-1+5x-2x+2x^2+7\\
=2x^2+5x-2x+7-1\\
=2x^2+3x+6$$

$$\\\frac{\sqrt4}{2*\sqrt{64}}\\\\
\frac{2}{2*8}\\\\
\frac{1}{8}\\$$

Seems like  the company forgot to enter the choices! 😋😂

The dog seems to be very good at representing melodys expression Hun?

Where are the choices?

Thanks Heureka 😃

see:

We did this yesterday. So look through the old posts.

I think it may have bren in the end of day  wrap. 

What is the volume of a cylinder with a diameter of 301mm and a height of 360mm?

diameter d = 3.01 dm

height h = 3.6 dm

$$\text{Volume }\ V = \pi*r^2*h = \pi*\left(\frac{d}{2}\right)^2*h = \pi *\frac{d^2}{4}*h \\\\
\small{\text{
$
V =\pi *\frac{3.01^2}{4}*3.6 \ dm^3
$
}}$\\\\$
\small{\text{
$
V =25.616829\ dm^3 = 25616829\ mm^3
$
}}$$

What's 2/3 + 4/5

$$\small{\text{
$
\frac{2}{3} + \frac{4}{5}$
}}
\small{\text{
$
=\frac{2}{3} *\frac{5}{5}
+ \frac{4}{5}* \frac{3}{3}
$
}}
\small{\text{
$
=\frac{10}{15}+ \frac{12}{15}
$
}}
\small{\text{
$
=\frac{10+12}{15}
$
}}
\small{\text{
$
=\frac{10+12}{15}$
}}
\small{\text{
$
=\dfrac{22}{15}$
}}$$

1/2*(2/3)^2 - 1/9

1/2* 4/9  - 1/9

2/9 - 1/9

1/9

that is the answer