How do you do conversions?

For example:
Convert 360 s to ms

The reliable way to do conversions is to do them as you learned in dimensional analysis; i.e., as the number you want to convert x a factor. The factor numerator/denominator is arranged so that the unit you want to convert to is in the numerator and the unit you are converting from is in the denominator. For example, there are 1000 ms in 1 s so the factor can be either (1 s/1000 ms) or it can be (1000 ms/1 s).

360 s x (1000 ms/1 s) = ??
If this isn't clear please reply but explain what you don't understand.

My teacher taught me a different way but it's very confusing. She used exponential notations.

For example, how many milligrams equals 1 gram?

she did:

x/1 milligram= (1.0g x 10^0g) 1 milligram/ [all over] 1.0 x 10^-6
which equals 1.0 x 10^6 milligram

Your teacher appears to be using a combination of ratio and proportion and exponential notation; however, I don't understand what you wrote.

It was supposed to be a ratio and using exponential notation and skipping a step in cross multiplying, but it's very confusing how she did it.

To convert units, follow these steps:

1. Identify the given unit: In this case, the given unit is seconds (s).
2. Determine the target unit: The target unit is milliseconds (ms).
3. Find the conversion factor: To convert seconds to milliseconds, you need to know the conversion factor between the two units. Since there are 1000 milliseconds in 1 second, the conversion factor is 1000 ms/1 s.
4. Write the conversion equation: Use the conversion factor to set up the conversion equation. In this case, it will be: 360 s x (1000 ms/1 s).
5. Simplify the equation: Cancel out the common unit (seconds) from the numerator and denominator.
6. Perform the calculation: Multiply 360 by 1000 to get the result.
360 s x (1000 ms/1 s) = 360,000 ms.

Therefore, 360 seconds is equivalent to 360,000 milliseconds.