1. Scientific Notation
Scientific Notation is sometimes called exponential notation.
SCI NOT is used when working with very large or very small numbers. Numbers that are extremely large or small are hard to use in calculations and we run the risk of making errors.

2. The mass of one gold atom is .000 000 000 000 000 000 000 327 grams.
Examples:
The mass of one gold atom is
grams.
One gram of hydrogen contains
hydrogen atoms.
Scientists can work with very large and very small numbers more more easily if the numbers are written in scientific notation.

3. Steps for writing very large numbers in Sci Not
Step 1 - Find the decimal point. If there is no decimal point, assume it is at the end.
Step 2 – Move the decimal point so that there is only one non-zero digit in front of it.
Step 3 – Rewrite the number with only two decimal spots after it then write “x 10” after it.
Step 4 – Count how many spots you moved the decimal. This is your power on the 10.

4. For example: 4.5 x 103 The coefficient is _________. 4.5
The number 4,500 is written in scientific notation as ________________.
The coefficient is _________.
4.5
The coefficient must be a number greater than or equal to 1 and smaller than 10.
The power of 10 or exponent in this example is ______. 3
The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

5. 137,000,000 can be rewritten as
1.37 X 108

6. Using scientific notation, rewrite the following numbers.
Now You Try
Using scientific notation, rewrite the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104

7. Steps for writing very small numbers in Sci Not
Step 1 – Find the decimal point.
Step 2 – Move it so that there is only one non-zero digit in front of it.
Step 3 –Rewrite the number with only two decimal spots after it then write “x 10” after it.
Step 4 – Count how many spots you moved the decimal. This is your power on the 10 only this time it is negative.

8. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers.
8.82 X 10-4
5.9 X 10-7
4 X 10-5

9. More Examples 4 X 10-4 2) 1.248 X 10-6 .000001248 3) 6.123 X 10-51)
4 X 10-4
2) X 10-6
3) X 10-5 4)
3.06 X 10-6 5)
8.92 X 10-4

10. Steps for going from Sci Not to Regular Numbers
When it is a positive exponent, find the power and move the decimal to the right that many places.
When it is negative, find the power and write that many zeros in front. The decimal goes after the first zero.

11. Convert these:
1.23 X , X 106 6,806,000

12. Try These
4,000 4 X X 103 2, X 106 6,123, ,000, X 108

13. Using Scientific Notation in Multiplication, Division, Addition and Subtraction
Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

14. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Multiplication
When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x Add the exponents
Answer: 6.7 x 102

15. Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Division
Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 by Subtract the exponents 6 - 2
Answer: 3.8 x 104

16. Addition and Subtraction
To add or subtract numbers written in scientific notation, you must….express them with the same power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.
5.8 x 103 = .58 x so .58 x x 104 =?
Answer: x 104