Tutoring physics or chemistry, you need to explain scientific notation.

Scientific notation is very easy to use; it was designed to be.  To start with, we need to realize the “everyday” way we write numbers is called “float” (aka “normal”).

Another point to bear in mind is that scientists commonly space numbers in groups of three.  Therefore, 0.03445 might also be written as 0.034 45.  Similarly, 3467 might be written 3 467.

Example:  write 34 200 in scientific notation.

Solution: 3.4200×10⁴

So we see that 34 200 is 3.4200×10⁴ in scientific notation.

Example:  write 0.024 132 in scientific notation.

Solution: 2.413 2×10^-2

The point to realize is that in scientific, you always write the decimal after the leftmost digit, then write x10^p. The value of p is the number of places you need to move the decimal to return to its “normal” place. If you need to move the decimal to the left, p is negative.

Going from scientific back to float is easy as well; an example or two may help solidify the whole idea.

Example: write 3.24×10^-5 in float.

Solution: The exponent tells us to move the decimal five jumps to the left.   It turns out the number is 0.000 032 4 in float.

Example: write 7.59×10⁶ in float.

Solution: The exponent tells us to move the decimal six jumps to the right. We arrive at 7 590 000 in float notation.

Good luck with this new way of seeing numbers.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.