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Scientific notation

Scientific notation

Author: Peter Anderson

- Demonstrate how to write a number in scientific notation

- Show examples of how to add/subtract/multiply/divide numbers written in scientific notation

How to do it by the decimal point moving method. 

The calculator method

The no calculator method

Check yourself

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The Easy Way

A simple, quick approach to notation. Don't be afraid to pause it and rewatch. It's kind of quick.

Why bother?

Scientific notation is a way of dealing with very large or very small numbers that does not involve writing zero over and over.  It achieves this by including a power of ten that keeps track of how many times the zero has been moved.  If it moves left the power goes up, if it moves right the power goes down.

10(number of places I moved the decimal point)

For the ten reasons on the end of your hands humans think best about numbers between 1 and 10.  Scientific notation accounts for this handicap.  It always includes a number between 1 and 10.  Move the decimal point to the right of the first not zero.

In chemistry, it is most frequently used to deal with the very small.  Atoms exist in the world of x10-10

If we wanted to compare the size of barium to bromine which is easier?

Barium               /             Bromine

0.000000000222 m    /    0.000000000098 m

2.22 x 10-10 m       /         9.8 x 10-11 m

In the first case the zeros confuse the eyes and make it hard to tell.

In the second case the exponent immediately shows bromine to be smaller than barium. 


How to make your calculator do it

The real question is how to make the calculator do it for you. This is the answer.
If your exponent is negative always use parentheses around the power on the graphing calculator. On the scientific calculator press the negative button last.

What do I do if the calculator breaks?


Take the numbers out of scientific notation.  The power of ten shows you how many places to move the decimal point.

Do column addition or subtraction normally.

Put the result back into scientific notation.


This is an old trick that they used to teach in math class and don't anymore for some reason.

1.  Multiply or divide the numbers and write the result.

2.  If you are multiplying add the exponents together and write the result.  If you are dividing subtract the exponents and write the result.

3.  Adjust the final result to a number between 1 and 10.

I'll show you a simple one, then a complicated one. 

9*103 * 4*102

9*4 = 36

103*102 = 10(3+2) = 105

So, 36 * 105, but that isn't scientific notation because the first number is bigger than ten. 

Decimal point needs to go one to the left, so 3.6*106 is the answer.

2.0*106 / 6.022*1023

2 / 6.022 = 0.332

106 / 1023 = 10(6-23) = 10-17

0.332 * 10-17 isn't scientific notation because the first number is less than one.

Decimal point needs to go one to the right so 3.32*10-18 is the answer.


Check yourself

You can check yourself on turning it into scientific notation, taking it out, multiplying/dividing, adding/subtracting.  I like this one because it tells you how your answer is wrong instead of just marking it wrong, quite helpful when learning.