1. Significant Figures and Scientific Notation

2. Measurement in the scientific method
The key to a good experiment is being able to make good measurements and record our data in the proper way.
If we do not make good measurements, we will have incorrect data. Incorrect data results in bad results and wrong conclusions.

3. What Makes a Good Measurement?
Accuracy –
how close your measurement is to the correct value
Precision –
how close one measurement is to all other measurements in the experiment

4. Error ALL MEASUREMENTS HAVE ERROR So what is error?
Error is a measure of how far off you are from correct
Error depends on a number of different factors, but the main source of error is the tools we use to make the measurements
The accuracy of a measurement is dependent upon the tools we use to make the measurement.

5. Error
When recording our measurement, we have to make a guess…the guess shows our error…the smaller the guess, the more accurate our measurement…
How long is the box?
I know the measurement is at least 5 cm… cm
But since there are not marks between the centimeters, that is all we know for sure…
So we guess…5.8cm, the last digit shows our guess
Since each person guesses different, the last digit shows our error

6. Error To Get less error, we use a tool with smaller guesses…
What is the measurement with a more accurate tool?
5.91 cm…the 1 is a guess

7. Minimizing Error
There are many ways to minimize your error in measurement, but the main ways are…
Using more accurate tools – since your measurement can only be as accurate as your tool, if your tool is more accurate, your measurement will be more accurate.
Avoiding parallax –
parallax is the apparent shift in location due to the position of an observer…
We avoid parallax by…(volunteers needed for demonstration)

8. Using Measurements
Since our measurements all have error, when we use them in calculations, we have to carry the error through…
How do we do this you ask?
Significant Figures…

9. Significant Figures
Significant figures are scientists way of showing accuracy in measurements and in calculations
JUST BECAUSE IT IS ON YOUR CALCULATOR SCREEN DOES NOT MAKE IT SIGNIFICANT!

10. Rules for Identifying sig. figs. In a Measurement
All non-zero digits are significant
1, 2, 3, 4, 5, 6, 7, 8, 9
Leading zeros are place holders and not significant
Trailing zeros are only significant if they are to the right of the decimal
 zeros are not significant
 zeros are significant
Zeros between two significant figures, or between a significant digit and the decimal are significant
101  zero is signigicant
10.0  all zeros are significant
 all zeros are significant

11. Significant Figures
So, is there an easy way to figure this out without memorizing the rules…
YES!

12. Sig Fig Tool
We will use our great nation to identify the sig figs in a number…
On the left of the US is the Pacific and on the right is the Atlantic P A

13. Sig Fig Tool
If we write our number in the middle of the country we can find the number of sig figs by starting on the correct side of the country…
If the decimal is Present, we start on the Pacific side
If the decimal is Absent, we start on the Atlantic side
We then count from the first NON zero till we run out of digits… P A

14. Sig Fig Tool Examples P
105200 A 4
This number has _____ sig figs

15. Sig Fig Tool Examples P
307.10 A 5
This number has _____ sig figs

16. Sig Fig Tool Examples P A 1
This number has _____ sig figs

17. Sig Fig Tool Examples P A 6
This number has _____ sig figs

18. Calculations with significant figures
Since our measurements have error, when we use them in calculations, they will cause our answers to have error.
Our answer cannot be more accurate than our least accurate measurement.
This means that we have to round our answers to the proper accuracy…

19. Rounding
Rounding is the process of deleting extra digits from a calculated number. 1. If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped rounded to three significant figures becomes If the first digit to be dropped is greater than or equal to 5, the excess digits are all dropped and the last significant figure is rounded up rounded to three significant figures becomes 62.9

20. Round The following 423.78 to three significant figures 424
B to two significant figures
C to four significant figures
22.55
D to three significant figures
(must have decimal)
E to one significant figure
0.4
F to three significant figures
7.21

21. Calculations with significant figures
When we add or subtract, our error only makes a small difference. So, when adding or subtracting we base our rounding on the number of decimal places.
Rule for Adding and Subtracting –
the answer must have the same number of decimal places as the measurement used in the calculation that has the fewest decimal places

22. Example 1
35.0 cm cm – 7 cm = ? cm This is what your calculator gives you… However, as we just discussed, the answer cannot be more accurate than your least accurate measurement… The least accurate measurement is 7 cm… So by the adding rule, our answer must be rounded to zero decimal places, or the ones place Which gives us the answer of 31 cm

23. Calculations with significant figures
When we multiply or divide, our error makes a large difference. So, when multiplying or dividing numbers, we round based on significant figures.
Rule for Multiplying and Dividing –
the answer must have the same number of significant figures as the measurement used in the calculation that has the fewest significant figures

24. Example 2
3.0 x ÷ = ? We have to round to proper sig figs… So we get Or in scientific notation (which we will discuss next) 3 x 1011

25. Example 3
What if we have both add/sub and mult/div in the same problem?
(2.4 m + 5 m) ÷ (1.889 s – 3.9 s) = ?
Order of operations means we do the addition and subtraction first…
(7.4 m) ÷ (-2.011s)
We have to round these before we go on to the division…
7 m ÷ -2.0 s
Now divide
m/s
Now Round
-3 m/s

26. Scientific Notation Use to express very large or small numbers
or x1023
or x10-19

27. Scientific Notation
Scientific (Exponential) notation is a system in which a number is expressed as a product of a number between 1 and 9 multiplied by 10 raised to a power (exponent).

28. Scientific Notation C x 10n
C= the coefficient= only the significant figures are used
n= the exponent (power)= location of the decimal point

29. Scientific Notation
1. The value of the exponent is determined by counting the number of places the original decimal point must be moved to give the coefficient. Remember that the coefficient must be a number from 1 to 10.

30. Scientific Notation
2. If the original number (in standard notation)is greater than 1, the exponent is a positive number.
or x1023
3. If the original number is less than 1, the exponent is a negative number.
or x10-19

31. Example 1 Write 628,000 in scientific notation
a. Determine the number of sig figs __ 3
b. Write the coefficient ____
6.28
c.Determine the number of places to move the decimal point __
 larger than 1 = positive exponent 5
Answer =
6.28 x 105

32. Example 2 Write 0.00260 in scientific notation
a. Determine the number of sig figs __ 3
b. Write the coefficient ____
2.60
c. Determine the number of places to move the decimal point __
 smaller than 1 = negative exponent
Answer =
2.60 x 10 -3

33. Write the Following in Scientific Notation
2305.7
x 103
3,000,000
3 x 106
300.
3.00 x 102
1.0 x 10-4
402.0
4.020 x 102
0.1005
1.005 x 10-1
3.57
3.57 or 3.57 x 100

34. Scientific Notation
To convert from scientific notation back to standard (ordinary) notation:
Simply move the decimal point the number of places indicated by the exponent.
Positive exponent= make number larger
Move decimal to the right 
Negative exponent= make number smaller
Move decimal to the left 

35. Write the Following in Standard Notation
a. 3.4 x b x c x d. 6.5 x e. 5 x 106 5,000,000

36. The overbar
You can make a zero in the middle of a number have significance by adding an overbar above it.
3,300 has 3 sig figs (or 3.30 x 103)
2,000,000,000 has 4 sig figs (or x 109)

37. Presentation created by: Mr
Presentation created by: Mr. Kern Information gathered from years of scientific research and data collection Assignment provided by : BHS Chemistry Department
THE END