1. Scientific Notation & Significant Figures
This stuff is boring, but we have to do it.

2. Scientific Notation
Scientists' way of being lazy.
Used for taking measurements of extremely large or small quantities.
Based on the power of 10 system.

3. 3 Parts to S.N.
1.) Coefficient: this is the actual number.
2.) Base: this is the ten
3.) Exponent: this is the power you are taking the ten to.

4. What you do to get scientific notation:
Take your number and multiply it by a power of ten, it's that easy.
RULES:
1.) Your coefficient must be between 1-10.
2.) If given significant figures in the problem, your scientific notation answer must include the right amount of sig. figs.

5. Let's get some practice:
Please write the number 602,000,000,000,000 in scientific notation:

6. Write the number .00000000000000000000876 in scientific notation:

7. Write the number 8.7902 x 108 in standard or real notation:

8. Write the number 5.00 x 10-12 in standard or real form:

9. Adding & Subtracting with S.N.
Steps:
1.) Get each of the coefficients in the same power (same exponent)
2.) Add or subtract the coefficients and keep the exponents the same.

10. Multiplying with S.N.
Steps:
1.) Multiply the coefficients together
2.) Add the exponents together

11. Dividing by S.N.
Steps:
1.) Divide the coefficients
2.) Subtract the exponents.

12. Please multiply 3.45 x 107 by 6.25 x 105 and please write your answer in correct scientific notation:
2.16 x 1013

13. Please add 3.76 x 104 and 5.5 x 102 and place it in correct scientific notation:

14. Please subtract 9.7 x 10 4 from 4.8 x 105 :

15. Please divide 3.5 x 108 by 6.6 x 104 :
5.3 x 103

16. Sig. Figs
This is a way for us to keep all our calculations standard. We want to always keep the same amount of significant figures in our answer as there were in our question.

17. Determining Sig Figs
In this class, you will be responsible for determining whether every number we calculate is significant...
When given a problem, first you should figure out what a problem is asking
You should then determine how many sig figs are in each number within the problem
The number with the most sig figs in the problem will give you the amount of sig figs needed in your answer

18. How do we determine what are sig figs?
Great question...there are rules for each individual number within a problem

19. 1.) All non-zero digits are significant
Rules for Sig Figs:
1.) All non-zero digits are significant
973 has 3 sig figs: the 9, 7, & 3.

20. 2.) Zeroes anywhere in between non-zero digits are significant:
has 5 sig figs
3.) Leading zeroes are not significant:
has only two sig figs.

21. 4.) Trailing zeroes in numbers with a decimal point ARE significant
has 5 sig figs
5.) Zeroes trailing at the end of numbers without a decimal point are not significant:
has 2 sig figs.

22. Rounding with Sig. Figs.
Steps:
1.) Find how many numbers you want to round to.
2.) Go to the most leftmost significant figure.
3.) Count over the number you want to round to and round after that number.

23. Example:
If I want to round to two significant figures I would take these steps:
1.) Find my leftmost sig fig (2)
2.) Count over two sig figs, including your leftmost figure and round there, giving me my answer: .026

24. Please round the following to 3 sig figs::

25. Round the following to 5 sig figs::

26. Round the following to 7 sig fig::