Scientific Notation: 32,400 or 0.000458 in sci. notation?

[HisWifey02]

How do you write 32,400 in scientific notation?

How do you put decimals in scientific notation such as 0.000458?

Also I have a problem that looks like this:
(4.2*10 to the -14th power just the ten though) (7.7*10 to the 11th power just the ten again)

How do I solve that?

 

[galactus]

Scientific notation isn't too bad. Generally, the leading constant is between 1 and 10.

So, if you have 32,400, you move your decimal however many places to the left so that you have 3.24. That would mean you move 4 places to the left and get

\(\displaystyle \L\\3.24\times{10^{4}}\)


For small numbers like 0.000458, you move the decimal however many places to the right so you have 4.58 and make the exponent of the 10 a negative.

To get 4.58, you move 4 places to the right and get \(\displaystyle \L\\4.58\times{10^{-4}}\)

See?. Ain't bad, is it?.

 

[arthur ohlsten]

32,400 = 3.24 times 10,000
32,400 =3.24x10^4

is this what you need?

.000458=458 divided by 1,000,000
.000458=4.58 divided by 10,000
4.58x10^(-4)



[4.2 x10^-14] [ 7.7 x10^11]
[4.2*7.7][10^-14*10^11]
when you multiply you add exponents
32.34[10^(-14+11)]
32.34 x 10^-4
3.234 x10^-3 answer

Arthur