Scientific Notation

Why Do We Need It?

• Chemistry deals with very large and very small numbers

•6.02 x 10 23 (Avogadro’s #) (lots of atoms)

•1.5 x 10 -10 (size of an atom)

The “Size” of the Numbers

• 0.00000000000000000000000000000000663– How do we keep track of all those zeroes?

• 0.00000000000000000000000000000000663 x 300000000000 / 0.0000009116– Worse yet… calculations with those numbers

Big and Small Numbers

• Better in Scientific Notation

• (6.63 x 10 –31 x 3.0 x 10 10) /9.116 x 10-8

• Now… more compact, better represents significant figures and is easier to calculate

This lesson will show you:

1. How to write numbers in scientific notation

2. How to convert to and from scientific notation

3. How to correctly do scientific notation on your calculator

4. How to calculate numbers in scientific notation

Format for Scientific Notation

• X = 1< N > 10 x 10 some positive or negative integer

• The decimal point is in correct location if it is behind the first non-zero digit.

• If 0< x> 1 the X = N x 10 negative number

• If 1< X < 10 then X = N x 100

• If X > 10 then X = N x 10Positive number

Examples

9.8

8.7 x 10-4 0.00087

23 000 000

9.8 x 100

2.3 x 107

First Explanation• Start at the decimal point of the original

number• Count the number of decimal places you

move to get to one place to the left of the decimal

• The number of places you move is the exponent. Left it’s a positive value…..right is a negative value

Second Explanation• Write all digits down with the decimal point

just to the right of the first significant digit. This should always result in a value between 1 and 10

• Now count how many decimal places you would move to recover the original number.

• If you count to the left the exponent is negative. To the right is positive.

Correcting Incorrect Scientific Notation

428.5 x 109

• Write the integer as a number between 1 and 10

• Correct the exponent

From Scientific to Decimal

Exponential notation

• 1.25 x 102

• 6.83 x 10-2

• 3.35 x 10-8

• 9.33 x 1012

Normal Notation

• 125

• .0 683

• .0 000 000 335

• 93 300 000 000

Math with Scientific NotationAddition and Subtraction

• All exponents MUST BE THE SAME before you can add and subtract numbers in scientific notation. The actual addition or subtraction will take place with the numerical portion, NOT the exponent.

• A good rule to follow is to express all numbers in the problem in the highest power of ten

Math with Scientific NotationMultiplication and Division

• Multiplication: Multiply the decimal portions and add the exponential portions.

• Division: Divide the decimal portions and subtract the exponential portions.

Examples

(3.05 x 106) x (4.55 x 10¯10) =

(3.05 x 106) + (4.55 x 104) =

(1.05 x 108) / (2.85 x 103) =

(9.33 x 10-13) - (4.55 x 10-14) =

1.39 X 10-3

3.10 x 106

3.68 x 104

8.88 x 10-13

Using Your Calculator

• Speaking realistically, the problems discussed can all be done on a calculator.

• However, you need to know how to enter values into the calculator, read your calculator screen, and round off to the proper number of significant figures.

• Your calculator will not do these things for you.

The EXP Key

• The right way involves the use of a key usually marked "EXP" or "EE." A usual wrong way involves using the times key, where the student presses times then 10 then presses the "EXP" key.

What to know about your calculator

• Be sure you know how to put your calculator into scientific notation.

• Be sure you know how to take it out of scientific notation.

• Know how you calculator reports exponents.