1. Scientific Notation
Cartoon courtesy of NearingZero.net

2. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

3. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
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4. Scientific Notation:
A method of representing very large or very small numbers in the form:
M x 10n
M is a number between 1 and 9
n is an integer equal to the number of decimal places moved

5. . 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

6. 2.5 x 109
The exponent is the number of places we moved the decimal.

7. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n

8. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

9. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
ADDITION AND SUBTRACTION

10. Review: M x 10n Scientific notation expresses a number in the form:
n is an integer
1  M  10

11. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106 7
x 106

12. If the exponents are NOT the same, we must move a decimal to make them the same.

13. 4.00 x 106
4.00 x 106
x 105
+ .30 x 106
4.30
x 106
Move the decimal on the smaller number!

14. A Problem for you…
2.37 x 10-6
x 10-4

15. Solution…
x 10-6
2.37 x 10-6
x 10-4

16. Solution…
x 10-4
x 10-4
x 10-4

17. Scientific Notation and your calculator
To enter a number in scientific notation on your calculator follow these steps:
#1 Type in the decimal number
- ex 6.022
#2 For most TI calculators press 2nd and then the EE button (usually above the x2 or x-1 buttons)
- This represents x 10n in calculator language
DO NOT TYPE IN x 10^n YOU WILL GET THE WRONG ANSWER!

18. List the value of the following exponential terms
__________ 1) 1.0 x 103 __________ 2) 1.0 x 100 __________ 5) 1.0 x 10-3

19. Put the following numbers into scientific notation.
__________ 6) __________ 7) __________ 8) 4,310,000 __________ 9)

20. Take the following numbers out of scientific notation
____________________ 10) 3.67 x 105 ____________________ 11) x 103 ____________________ 12) 3.1 x 10-1 ____________________ 13) 5.04 x 10-5 ____________________ 14) 2.00 x 100

21. Put the following numbers into correct scientific notation f sig figs indicated
________ 15) 30,000 (3 sig figs) ________ 16) 115,000,000 (2 sig figs) ________ 17) 106,000 (4 sig figs) ________ 18) (3 sig figs) ________ 19) (2 sig figs) ________ 20) (3 sig figs)

22. Solve the following problems
Solve the following problems. Put the answers into correct scientific notation form. (Yes, sig figs matter.)
________ 21) 1.50 x 102 / 2.39 x 10-1 ________ 22) 3.29 x 105 / 2.1 x 106 ________ 23) 1.50 x 104 * 2.3 x 10-3 ________ 24) x 10-3 * 2.67 x 101 ________ 25) 2.60 x 106 * 1.50 x 10-2