1. Scientific Notation with positive powers of 10
Lesson 2.2
Mrs. Carley

2. Definition of Scientific Notation
Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10 and a power of 10.

3. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 9
and n is an integer

4. Example I
Write 4,776 in scientific notation
Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between one and ten.
4.776
Count the number of digits between the old and the new
decimal point, this gives the power, n of 10 (10n).
4 776
3 Digits
X 103
Since the decimal is shifted to the left, the exponent is positive.
4.776 x 103

5. Writing a number in Standard Notation Example #2 Video

6. Write the decimal number.
Example #2
Write x 104 in standard form
Write the decimal number.
4.953
Move the decimal the number of places specified by the powers of ten: to the right since it is positive.
4 9530
X 104
4 Places
Rewrite the number in integer/standard form.
49,530

7. Scientific notation with Negative Powers of 10
Lesson 2.3
Mrs. Carley

8. RULES Writing numbers in Scientific Notation
When I move the decimal to the right the exponent is negative.
When I move the decimal to the left the exponent is positive.
Writing numbers in Standard Notation
When I move the decimal to the right, the number is positive
When I move the decimal to the left, the number is negative.
HINT: Think about the number line

9. Example #1
The average size of an atom is about centimeters across. Write the average size of an atom in scientific notation.
Step 1: Place the decimal point
Step 2: Count the number of places you moved the decimal point.
Step 3: Any time you move the decimal point to the right….the exponent to the power of 10 is negative.

10. Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

11. Write 28750.9 in scientific notation.
x 10-5
x 10-4
x 104
x 105

12. Write 531.42 x 105 in scientific notation.

13. Writing a Number in Standard Notation
Example #2

14. Example #2
Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10-6 in standard notation.
Step1: Use the exponent to the power of 10 to see how many places to move the decimal point.
Step 2: Place the decimal point. Since you are going to write a number less than 2.33, move the decimal point to the left. Add place holder zeros if necessary.
Answer:

15. Write the decimal number.
Another Example
Write x 10-1 in standard form
Write the decimal number.
8.397
Move the decimal the number of places specified by the powers of ten: to the left since it is negative.
X 10-1
1 Place
Rewrite the number in integer/standard form.
0.8397

16. Express 1.8 x 10-4 in decimal notation.
Express 4.58 x 106 in decimal notation.
4,580,000

17. Operations with Scientific Notation
Lesson 2.4
Mrs. Carley

18. Adding/Subtracting Numbers
Look at Example#1:
Step1: Write each number in standard notation
Step2: Complete the operation – add/ subtract
Step3: Write the answer in scientific notation
Complete #1 “Your Turn” on page 52.

19. Multiplying Numbers in Scientific Notation
Multiply: (5.1 * 104) x (2.3 * 106)
Multiply the coefficients: 5.1 * 2.3 = 11.73
Add the powers of 10: 4+6 =10
Check to be sure the product is in scientific notation. (5.1 * 104) x (2.3 * 106) = * 1010
1.173 * 1011
Therefore, (5.1 * 104) x (2.3 * 106) = * 1011

20. Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

21. Dividing Numbers in Scientific Notation
Divide (3.9 * 108)
(6.5 * 10-4)
Divide the coefficients: 3.9 / 6.5 = 0.6
Subtract the powers of 10: 8 – (-4) = 12
Check to be sure the quotient is in scientific notation.
(3.9 * 108) = 0.6 * 1012)
6.0 * 1011

22. Example #2 Page 52
Complete #2-3 “your Turn”