Scientific Notation

How to cope with really big and really small numbers…

The setup

In chemistry, we deal with numbers that are often times too big to put into a calculator.

Ex:602 200 000 000 000 000 000 000

So how do we manage them?

The secret is the decimal, and factors of 10.

101 = 10 102 = 100 103 = 1000 104 = 10,000 Etc…

So… 5 x 103 = 5 x 1000 = 5000 And… 60,000 = 6 x 10,000 = 6 x 104

Converting to Scientific Notation

Start with a number. 13 000 000

Move the decimal to the right of the first digit. 1.3 000 000

Count the spaces you moved left: This is your power of ten. 1.3 x 107

Trim off extra zeros on the right

Let’s try a few

65,000

423,000

32,000,000

6.5 x 104

4.23 x 105

3.2 x 107

And backwards…

3.45 x 104

5.437 x 107

3.33 x 102

34,500

54,370,000

333

What about decimals?

.000 000 0023 This is handled in the same way, but with a

negative exponent 2.3 x 10-9

Let’s try a few

.00345

.000 056 7

.000 005467

3.45 x 10-3

5.67 x 10-5

5.467 x 10-6

Remember!

Negative exponents equate with numbers less than one.

Positive exponents equate with numbers that are larger than one.

Some simple rules

Only one digit is allowed to the left of the decimal when in scientific notation.

The exponent on the ten has to equal the number of spaces the decimal moves.

Assignment

Page 50-52 72-76,79,80,93

Show fences and rails for any metric conversions