1. Warm-Up 9/9/13
Write down the following pairs of numbers:
3.2 x 104 and 32,000
and 4.7 x 10-6
65,000,000 and 6.5 x 107
Use <, >, or = to compare the value of the numbers.
Use your table partners for help, and make your best guess if you are unsure!

2. Scientific Notation
Monday 9/9/13

3. Why Scientific Notation?
Used to express very large numbers and extremely small numbers in a shortened form.
Examples (from warm-up):
3.2 x 104 = 32,000
= 4.7 x 10-6
65,000,000 = 6.5 x 107

4. Scientific to Standard Form
From scientific notation, we can determine the original form of the number.
The exponent tells you how many times to move the decimal to get back to “standard” form.
102 is the same as 10x10, or moving the decimal right twice
104 is the same as 10x10x10x10 or moving the decimal right four times

5. Two Types of Exponents Positive Negative Ex) 6.7 x 105
Rule for Re-writing:
If an exponent is positive, the number gets larger, so move the decimal to the right.
Ex) 6.7 x 10-5
Rule for Rewriting:
If an exponent is negative, the number gets smaller, so move the decimal to the left.

6. Examples
What is 8.2 x 105 in standard form?
+5 exponent means multiplying by 10 five times! OR moving decimal right five times.
820,000
What is 1.3 x 10-4 in standard form?
-4 exponent signals the standard form number is small. We move the decimal left four times.
.00013

7. Try These!
Change these numbers to standard form (you have one minute!)
9.7 x 10-6
4.4 x 109
4,400,000,000

8. Standard to Scientific Notation
To put a number into scientific notation:
Move the decimal until there is one digit (1-9) in front of it.
410,000 becomes or 4.1
Take the number from step 1, and add x10 after it.
4.1 x 10

9. Count the number of times you had to move the decimal in step 1
Count the number of times you had to move the decimal in step 1. This is the value of the exponent.
4.1 x 10 5
If you moved right, the exponent is negative. If you moved left, the exponent is positive.
4.1 x 10+5

10. 5.5 x 10-4 (we moved right, so negative exponent)
Another Example
Write in scientific notation.
5.5
5.5 x 10
5.5 x 104
5.5 x (we moved right, so negative exponent)

11. Your Job With one other person, complete the matching activity.
Cut out all cards
Match the standard and scientific form
Match the sets of numbers to the object that is closest to that size
(You should have three cards in each set)
When done, check your answers with me 
Homework: Start Math Quest Review
Math “Quest” on Wednesday!