Lesson 4: Scientific Notation

In the last section you learned how to use sig digs in your calculations.

To get around these problems, we use Scientific Notation (sometimes called Exponential Notation).

Example 1:

105 = 10 x 10 x 10 x 10 x10 = 100 000

10-5 = 1/10 x 1/10 x 1/10 x 1/10 x 1/10 = 0.00001

Don't worry about spending half a minute using your calculator to figure out what 105 equals. Instead, notice that 105 written out has five zeros.

Converting Numbers into Scientific Notation

When you decide to use scientific notation, follow these rules. We'll try them out on the numbers from the start of the lesson ...

  1. Move the decimal over so that only one non-zero number is to the left of the decimal.

4 500 000 000 -> 4.500 000 000

0.000 000 010 -> 000 000 01.0

  1. Count how many spaces over you moved the decimal. If you moved it to the left it's positive, if you moved it to the right it's negative.

4.500 000 000 -> moved 9 spaces left (+9)

000 000 01.0 -> moved 8 spaces right (-8)

  1. Get rid of any numbers that are not sig digs. This might depend on the numbers you used in your calculation.

4.500 000 000 -> 4.5
I'm assuming that all those other zeros were probably just place holders, although I'd need a reason to do this in a real question.

000 000 01.0 -> 1.0
I'll keep this last zero. Since it was written in the original number for such a small number, it's probably significant.

  1. Write down the number, multiplied by 10 to the power of however many spaces you found in step 2.

4 500 000 000 = 4.5 x 109

0.000 000 010 = 1.0 x 10-8

If you ever need to change a number in scientific notation back to regular form, do the reverse of the above.

When you do this, you might be writing a number down with more sig digs than it actually has. The only time you should do this is if your calculator can't do exponents.

Scientific Notation on Your Calculator

Most calculators now have a key on them for doing scientific notation. Look for one of the following...

Do NOT use the "hat" symbol on your calculator to enter scientific notation (eg. 4.5 x 10^5).

On your calculator, type in the question as it's written.

Example 2: Try doing this on your calculator. See if you get the same answer.

4.587 x 104 ÷ 1.2 x 10-3 = 3.8 x 107

If you're using a TI graphing calculator, you'll notice that it shows scientific notation with an "E" (for exponent). The above example would look like this on your display...

To make typing scientific notation easier for me on this site, I will be using a style similar to the way a TI-83 would show the numbers. For example, I'll be typing 4.587e4 instead of 4.587 x 104. Hope ya' don't mind.

It's really easy to mix up typing a set of numbers on your calculator using scientific notation. Click here to watch a video on the proper method. I'm using a Casio calculator, but it's the same sort of ideas on most calculators.