Regents Physics

Scientific Notation PowerPoint Lecture Notes

Scientific Notation

Why do we use it?

Very Small things... BIG THINGS

Scientific Notation

What can the number 10 do?

It can be used as a multiplier or a divider to make a number LARGER or smaller

Example: 1.0 x 10 = 10 x 10 = 100 x 10 = 1000

AND

Example: 1.0 / 10 = 0.10 / 10 = 0.010 / 10 = 0.0010

Scientific Notation

Scientific notation uses this principle…– but…uses a shorthand form to move the

decimal point

The “shorthand” form is called THE POWERS OF 10

The Powers of 10

1.0 x 10 x 10 = 100…right?!

1.0 is multiplied twice by ten…

– therefore 10 x 10 = 102

This is called an exponentand is written EE on your calculator!

The Powers of 10

Overall.. 1.0 x 100 = 1.0 x 102 = 1000 We can also look at it a different way..

1000 has three zeros after the digit 1..so..

it takes three moves to the right to get to the end of the number!

The Powers of 10

1 0 0 0

3 moves to the right gives a positive exponent

1.0 x 103 = 1000 also!

Moves to the right make a number larger... But what about moves to the left?

1.0

The number gets smaller!

Moves to the left

0.01 = 2 moves from 1.0 to the left therefore..

1.0 x 10-2

The negatives sign means move decimal to the left!

The Powers of 10 Summary

Moves to the right are positive and

make a number larger!

Moves to the left are negative and

make a number smaller!

The number with the decimal > 9.99..etc

and cannot be smaller than 1.0

Practice Problems

Convert to Scientific Notation

10000

50000

565,000

0.0036

0.00000887

1.0 x 104

5.0 x 104

5.65 x 105

3.6 x 10-3

8.87 x 10-6

Convert to regular numbers

2.3 x 105

5.3 x 103

6.75 x 10-4

3.19 x 10-9

Practice Problems

230,0005300

0.000675

0.00000000319