Question

0.000027 is 2.7 * 10^(-5), so would it also be 27 * 10^(-4 )or 27 * 10^(-6? )

Answer 1

27 * 10^-6

You are placing the decimal point after 27 --- 27.
And then shifting the decimal point to the left with zeros

Answer 2

Sorry, but I don't know.

Answer 3

I assume you are dealing with numbers in scientific notation.
Such a number consists of a decimal number between 1 and 9 inclusive, multiplied by a power of 10
e.g.
3.45 x 10^7
4.123 x 10^-3
etc

so 0.000027 = 2.7 x 10^-5
Notice I moved the decimal place to the RIGHT by 5 places, resulting in the 10^-5

Observation: 10^-5 is a "small" number
by changing .000027 to 2.7 , I made it bigger, so to compensate I multiplied by a smaller.
Had it been 4567.8
it would be 4.5678 x 10^3

Another way to look at:
4567.8 ---- we have a large number, so it need a power of 10 with a positive exponent
.000027 ---- we have a small number, so it need a power of 10 with a negative exponent

Answer 4

1 ≤ n < 10 ... slight adjustment to Reiny's "definition"