Scientific Notation Notes

You will need your own paper.

Purpose:Often in science we work with numbers that are really small or really big. Not wanting to spend a lot of time writing zeros, we use scientific notation instead. Scientific notation works on powers of ten, making the zeros that we don’t want to write the exponents of ten.

Examples: 1,000,000 = 1 x 106

10,000 = 1 x 104

100 = 1 x 102

10 = 1 x 101

0.1 = 1 x 10-1

0.01 = 1 x 10-2

0.0001 = 1 x 10-4

0.000001= 1 x 10-6

Examples:A. 35,000 = 3 . 5 0 0 0. = 3.5 x 104

B. 0.0042 = 0 . 0 0 4 . 2 = 4.2 x 10-3

C. 0.0000815 = 0 .0 0 0 0 8 . 1 5 = 8.15 x 10-5

Note: the decimal gets moved behind the first nonzero digit - ALWAYS!

To take a number out of scientific notation just reverse the direction the decimal has moved

Significant Digits and Scientific Notation

Keep the Sig Digs the same!

In scientific notation it is the significand (the front part) that contains the significant digits. Again, nothing after the “x” sign counts towards signifcant digits.

5.423 x 109 has 4 sig digs9.0 x 10-4 has 2 sig digs1.0000008 x 102 has 8 sig digs

When converting into or out of scientific notation you MUST KEEP THE SIG DIGS THE SAME.

Try These:Turn these into scientific notation:A) 405,000B) 0.00203C) 0.009000D) 40

Turn these into standard notation:E) 7.601 x 106

F) 4.20 x 10-3

G) 1.0000 x 102

Try These:Turn these into scientific notation:A) 405,000 4.05 x 105

B) 0.00203 2.03 x 10-3

C) 0.009000 9.000 x 10-3

D) 40 4 x 101

Turn these into standard notation:E) 7.601 x 106 7601000F) 4.20 x 10-3 0.00420G) 1.0000 x 102 100.00

Using Scientific Notation in a Calculator

It’s not like you think…

You must communicate with the calculator in the way it was meant to communicate. This is most important with scientific notation.

For example: 6.022 x 1023 ÷ 2.52 x 1014 = ?

Instead of using “x 10^” the calculator needs the “EE” button. On the screen you would see:

6.022E23÷2.52E14, and it would equal 2.39E9, which you would write down as 2.39 x 109.

Without the “EE” button you’d get the answer 2.39 x 1037 - which is completely wrong.

A Final Thought About Scientific Notation

Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?

Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?

Scientific Notation to the rescue!

Lets say I counted 100 Skittles, and wanted to report this to a friend. He would think I rounded to the hundreds place, but I counted each skittle and know it to the ones place. How do I show this?

Because I want the ones place to be a significant digit it will report it as 1.00 x 102. Now both zeros are significant and my friend knows I rounded to the ones place.

Try These:

Round 4,500,000 to four sig digs.

Round 0.002 to three sig digs.

Try These:

Round 4,500,000 to four sig digs.4.500 x 106

Round 0.002 to three sig digs.

Try These:

Round 4,500,000 to four sig digs.4.500 x 106

Round 0.002 to three sig digs.2.00 x 10-3