1. When would someone think of using scientific notation?

2. You guessed right!
Scientific Notation is used when the actual numbers are too LARGE or too small.
Mostly in science
Small numbers from items impossible to see with the human eye
Large numbers too big to fit on the page
Makes calculations easier.

3. How to write in Scientific Notation
Get your number to be between 1 and 9 by moving the decimal to the left or right.
1,624,000,000,000,000 changes to

4. How Many Spaces?
Count the number of spaces from the beginning decimal point to the new point.
Ex ,000,000,000,000 (15 spaces)

5. Moving the Decimal Point
Copy all the whole numbers with the new decimal point : 1.624

6. Power of Ten
Multiply the remaining number by 10 raised to the number of places the decimal point moved.
1.624 x 1015

7. Positive Exponent
Use a positive exponent if the decimal point moved to the left.
392,000.
3.92 x 100,000
3.92 x 105
A large number to a smaller number - positive exponent

8. Negative Exponent
Use a negative exponent if the decimal point moved to the right.
4.32 x 10 -6
A small number to a larger number is a negative exponent.

9. Your Turn
1.) 29, ) 222.6
2.) ) 2,230,000
3.) )
4.) ) 17,250

10. Answers
1.) 29,900 5.) x x ) ) 8,230, x x ) ) x x ) ) 17, x x 104

11. If given the information in SCIENTIFIC NOTATION how do you write out the number?
EX x 104 = ? STEP 1- Write the whole numbers with the decimal STEP 2- If there is a POSITIVE exponent, count the number of spaces to the RIGHT of the decimal point to match the exponent = 12500

12. 6.4 x 10-3
STEP 3- If there is a NEGATIVE exponent, count the number of spaces going to the LEFT of the decimal point to match the exponent. =

13. TRY THESE! Rewrite these numbers so they are no longer in scientific notation.
1.) x ) (105)
2.) x ) (10-5)
3.) 5.6 X ) 4.22 x 102
4.) 9.7 x ) 8.96 x 103

14. ANSWERS
1.) x ) (105)
,586.
2.) x ) (10-5)
37,
3.) 5.6 X ) 4.22 x 102
4.) 9.7 x ) 8.96 x 103
97,000, ,960

15. Computing in Scientific Notation
Example: x 32,000,000 x
Step 1- Write the numbers in Scientific Notation.
6 x x x x 4.3 x 10-3
Step 2- Use the commutative property to change the order of the factors.
6 x 3.2 x 4.3 x 10-7 x 107 x 10-3.

16. 6 x 3.2 x 4.3 x 10-7 x 107 x 10-3.
Step 3- Complete the multiplication, using the rule for multiplying with exponents.
6 x 3.2 x 4.3 = 82.56
10-7 x 107 x 10-3 = 10( ) =10-3
Answer: x 10-3
Step 4- Write the product in scientific notation.
82.56 x 10-3= x 10(-3+1)=
Answer: x 10-2

17. YOUR TURN
1.) x x ) (11,000,000)2

18. TO FIND THE QUOTIENT: 9,250,000 divided by 25,000
Step 1- Write each number in scientific notation.
9.25 x x 104
Step 2- Rewrite the division as a fraction.
9.25 x 106
2.5 x 104

19. 9,250,000 / 25,000
Step 3- Complete the division, using the rule for dividing with exponents.
9.25 x 106 = 9.25 x 106 = 3.7 x 102
2.5 x
Step 4- Check that the product is written in scientific notation.
3.7 x 102

20. YOUR TURN
1.) 350,000 divided by 1,400,000

21. Answer
350,000 / 1,400,000 1.) 3.5 x 105 / 1.4 x ) 3.5 x x ) 3.5 x 105 = 3.5 x 105 = 2.5 x x ) 2.5 x 10-1

22. Using your calculator to solve Scientific Notation Problems
Push MODE
Scroll to SCI (scientific notation)
2nd MODE (Quit)
Put number into calculator ENTER
E means “time 10 to the power of”
Ex. 40,000,000 = 4E7 = 4 x 107

23. Scientific Notation Open Ended Question
Consider this multiplication expression.
(3.2 x 104) (3 x 103)
Set your calculator in scientific notation mode and evaluate this expression.
Explain how you could do the multiplication above without using a calculator.
Find the product (2.1 x 106) (4 x 105) and write it in scientific notation.