1. Significant Figures, and Scientific Notation
The valid measurements or digits are called SIGNIFICANT!

2. When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer.

3. Significant figures are all the digits in a measurement that are known with certainty
plus a last digit that
must be estimated.

4. Uncertainties of Measurements
Accuracy is the degree of “exactness” to which the measurement quantity can be reproduced.

5. Accuracy
Is the extent to which a measured value agrees with the standard value of the quantity.
CALCULATORS DO NOT INCREASE THE ACCURACY!

6. Using Significant Figures reflects precision by estimating the last digit
What is the certain measurement? (52 ml)
What is the estimated measurement? (.8 ml)

7. The instrument determines the amount of precision of the data.
What is the certain measurement here? (62.4 g)
What is the estimated measurement here? (.00 g)

8. Error vs. Mistakes ERROR MISTAKES Mistakes are caused by PEOPLE
Scientific errors are caused by INSTRUMENTS
Scientific measurements vary in their level of certainty
Mistakes are caused by PEOPLE
Misreading, dropping, or other human mistakes are NOT error

9. Significant Digits Nonzero digits are always significant
All final zeros after the decimal point are significant
Zeros between two other significant digits are always significant
Zeros used solely for spacing the decimal point are not significant

10. Exact and Counting Numbers do not have significant digits

11. Exact numbers are important: they are infinitely valuable
Exact numbers are important: they are infinitely valuable. Counting numbers come only in whole numbers.

12. There are rules for: multiplication/division addition/subtraction and combined equations

13. The answer can’t be more precise than the question
Rules for multiplication/division The result has the same number of significant figures as the factor with the fewest significant figures
The answer can’t be more precise than the question

14. The answer can’t be more precise than the question
Rules for addition/subtraction The result has the same number of decimal places as the number with the fewest decimal places
The answer can’t be more precise than the question

15. 1. Do the functions in parenthesis
2. Note the number of significant digits in the question
3. Perform the remainder of calculations
4. Round the final answer

16. Calculations Addition/Subtraction Multiplication/Division
The answer is based on the number with the fewest decimal points
Multiplication/Division
The answer is based on the number with the fewest significant digits

17. Round only the final answer in a series of calculations

18. Now You Try It! Add 24.686 m +2.343 m + 3.21 m = ?
Calculator says:
3 decimals, 3 decimals and 2 decimals
So 2 decimals it is
Answer is m
Multiply 3.22 cm by 2.1 cm
Calculator says
3 sig figs, 2 sig figs So 2 it is!
Answer is 6.8 cm2

19. Divide .005673 L by 2.1 L Calculator says 0.0027014286
4 sig figs and 2 sig figs
2 it is!
Answer is L

20. Scientific Notation
In chemistry we often use very large or very small numbers
We also have to pay attention to significant figures
Scientific notation allows us to do both easily!

21. Scientific Notation is using powers of ten
1000 becomes
1 X 10 3
becomes
1 X

22. Try These
3.45 x 104
2.36 x 10-3
5.69 x 107
x 10-7

23. How to do problems with scientific notation Ex. 4. 7 x 10 25 x 1
How to do problems with scientific notation Ex. 4.7 x x 1.9 x
first do numbers: 4.7 x 1.9
estimate as 5 x 2 = 10
now do powers: x = 12
so 10 x or 1.0 x 10 13

24. Calculators can help First, type in the number (ie 4.5) Then press 2nd
Finally, press EE
(above the comma)
The number will display
as 4.5 E 13
Read this as 4.5 x 10 13

25. Significant figures are easy when using scientific notation 2
Significant figures are easy when using scientific notation 2.3 x has 2 sig figs 3.7 x has 2 sig figs The placeholder zeros are eliminated for you!