Question

can somebody help me with scientific notations

Answer 1

If you post your question it would be AWESOME!:)

Answer 2

Think about splitting it all apart, and doing the coefficients separate from the powers, so

\[ \left( \frac{4*6}{1.2} \right) \left( \frac{10^5 * 10^{23}}{10^2}\right) \]

What are the left and right sides of that?

Answer 3

oh, your answer is correct for the record.

Answer 4

i dont get it at all though its by luck that that answer is correct because i accidentally clicked it can you tell me how to do it in steps ill fan and medal

Answer 5

@AllTehMaffs

Answer 6

So, if you have something like
\[2x10^3\]
that's the same as saying
\[2x10^3 = 2*1000=2000\]
That's probably boring.


Then next, if you have a some number to an exponent multiplied by one of the same number with an exponent, you can "add" the exponents! Like
\[2^2*2^2 = 2^{2+2} = 2^4 \ \ \ \longrightarrow \ \ \ 2^2*2^2 = 4*4 = 16 = 2^4\]
or
\[2^2*2^3*2^4 = 2^{2+3+4} = 2^9\]
and dividing by the same number with an exponent you can treat as subtraction of the powers
\[\frac{2^3*2^5}{2^4} = \frac{2^8}{2^4} = 2^{8-4}= 2^4\]
shown by
\[\frac{2^3*2^5}{2^4} = \frac{8*32}{16} = \frac{256}{16} = 16 = 2^4\]


Lastly, we have to remember our commutative property of multiplication, so
\[a*b*c = b*c*a = b*a*c\]
which applies if we're looking at scientific notation as shown above
\[2x10^3 = 2*1000 \ \ \ \ \longrightarrow \ \ \ \ \text{useful because} \ \ \]
\[ (2x10^3)(2x10^2) = (2*1000)(2*100) = (2*2)(1000*100) = 4*100000 = 4x10^5 \]
aka
\[(2x10^3)(2x10^2) =(2)(10^3)(2)(10^2)\]
\[= (2*2)(10^3 * 10^2) = (4)(10^{3+2}) = (4)(10^5) = 4x10^5\]

So finally, if we put everything together for the problem at hand, we take out all of the numbers in front of the " x10^ " and multiply them together, then multiply together all of the exponents
\[\frac{(4x10^5)(6x10^23)}{1.2x10^2} = \left( \frac{4*6}{1.2} \right) \left( \frac{10^5*10^{23}}{10^2} \right) \]
\[= \left( \frac{24}{1.2} \right) \left(\frac{10^{5+23}}{10^2} \right) = (10)(10^{28-2})= (10)(10^{26}) \]


Holler if you have any questions ^_^