Melody

"real number" was not specified either!

Perhap anonymous wanted to know how many sun glasses came after a trillion.

Answer.  A lot becasuse Sir CPhill gets them for free and he leaves them lying around EVERYWHERE!

I bet there are hundreds in those cupboards!

And Sir CPhill - there is no point arguing with me because I am a woman and therefore you have less than 5% chance of winning! And I am Queen of Camelot so you have no chance of winning.

And here are some more of those glasses that you keep losing!  

Please try to take better care of them!

Lady Guinevere.

Queen of Camelot

Otherwise known as the dinosaur!

Yes but you cannot find another integer in between a trillion and a trillion and one no matter what cupboard you look in.

Can you CPhill?        And I've got your sunnies!

Hi Sasini,

$$sin[\frac{\pi}{4}+A]*sin[\frac{\pi}{4}-A]\\\\
=[sin\frac{\pi}{4}cosA+cos\frac{\pi}{4}sinA][sin\frac{\pi}{4}cosA-cos\frac{\pi}{4}sinA]\\\\
\mbox{The two brackets are the same except one has a minus and the other a plus so this simplifies to the difference of 2 squares}\\\\
=[sin\frac{\pi}{4}cosA]^2-[cos\frac{\pi}{4}sinA]^2\\\\
=[sin^2\frac{\pi}{4}*cos^2A]-[cos^2\frac{\pi}{4}*sin^2A]\\\\
=[\frac{1}{2}cos^2A]-[\frac{1}{2}sin^2A]\\\\
=\frac{cos^2A-sin^2A}{2}\\\\
or\qquad
=\frac{1-2sin^2A}{2}\\\\
or\qquad
=\frac{cos2A}{2}$$

I got the same as well 

(((4x-)^6y)^5)^2)

Puttin a minus sign there does not make sense Sasini.  

Firstly standard form is another name for scientific notation.

It is easiest to conver everything to metres first

0.03*0.055*0.04

$${\mathtt{0.03}}{\mathtt{\,\times\,}}{\mathtt{0.055}}{\mathtt{\,\times\,}}{\mathtt{0.04}} = {\mathtt{0.000\: \!066}}$$

= 6.6 x 10^-5  m³

It is 6.6 because you have to have one non-zero digit  in front of the decimal point.

It is 5 because I moved the decimal point 5 places.  It is negative because it is a very little number. 

A trillion and one  

Aziz is correct 

I prefer to think of it as multiplying both sides by (x-2) and multiplying both sides by x

Equation must stay balanced.  What you do to one side you must do to the other side as well.

okay so now you have an answer for 69 and 96 lol

Thanks Aziz for that great explanation.

I just thought i would show how the cancelling is done in fraction form.

(I am playing with LaTex,  some of this is a bit new for me  )

$$\dfrac{9x^5y^4}{4y}\times\dfrac{2y}{3x}\\\\\\
=\dfrac{\not{9} \textcolor[rgb]{0,0,1}{^3} x^{\not5 \textcolor[rgb]{0,0,1}{4}} y^4}{\not{4}\textcolor[rgb]{0,0,1}{^2}\not{y}}\times\dfrac{\not{2}\not{y}}{\not{3}\not{x}}\\\\\\\
=\dfrac{3x^4y^4}{2}$$

0.125340000

First of all all trailing 0s after a decimal point have no value so

0.125340000=0.12534

Now you have to put one non-zero number in front of the point so that would be 1.2534

0.12534 is a llittle number - less than 1 so the index (exponent) will be negative.

To move the point from 0.12543 to 1.2543 you had to jump the point over 1 number (the 1) 

so the answer is  1.2534 x 10^-1