1. Science Math Lesson 2: Scientific Notation and Conversions

2. I. Scientific Notation
There are basically two ways to express written numbers:
1. Decimal Notation: traditional method of writing numbers
Examples: 5
250
6.7
1,952
2. Scientific (Exponential) Notation: a method of writing very large or very small numbers
Examples: 5 x 100
2.5 x 102
6.7 x 100
1.952 x 103

3. The exponent is referred to as the
Vocabulary
Exponent
Decimal number
1.23 x 106
Base
The exponent is referred to as the
POWER.

4. Positive exponents usually represent number greater than 1 or large numbers
For example: 12,345 = 1.23 x 104
Negative exponents usually represent number less than 1 or small numbers
For example: = 1.23 x 10-4
An exponent of “0” is simply the number itself which is why we do not usually use it
For example: 2.4 x 100 = 2.4

5. Practice! Turn your notes over. Can you fill in the blanks?
Decimal notation
Scientific notation
127
1.27 x 102
0.0907
9.07 x 10 – 2
5.06 x 10 – 4
2.3 x 109

6. II. Dimensional Analysis
Dimensional analysis (also known as the factor-label method or unit-factor method)
What this is all about is just conversion—converting one thing to another. This is something you will have occasion to do in real life. This is seriously useful stuff.
We're talking about measurable stuff, stuff you can count. Anything you measure will have a number with some sort of "unit of measure" (the dimension) attached. A unit could be miles, gallons, miles per second, peas per pod, or pizza slices per person.

7. Basic Steps for DA Step 1: Identify the WANTED unit (answer)
Step 2: Identify the GIVEN unit (starting point)
Step 3: Multiply the units STRAIGHT ACROSS so that all units cancel except the units needed for the final answer
Step 4: Check for correct units and round as needed

8. WANT-number of pizzas needed GIVEN-15 people need 4 slices each
Let’s Practice!! Turn your notes over. 1. How many seconds are in an hour? WANT-seconds per hour GIVEN-1 Hour 1 hour =
60 minutes
60 seconds
3600 sec
1 hour
1 minute
2. You have invited 15 people to a pizza party. You want every person to have 4 slices to eat. Each pizza has 12 slices. How many pizzas do you need?
WANT-number of pizzas needed
GIVEN-15 people need 4 slices each
1 pizza =
4 slices
15 persons
5 pizzas
1 party
12 slices
1 person
1 party