1. Unit 1: Basics // Metrics & Matter
Thursday, September 11, 2014
Unit 1: Basics // Metrics & Matter
Essential Question: How do scientists express the degree of uncertainty in their measurements?
Because nothing in science is ever certain…

2. Do Now
Use the ruler you have been given to measure the short side of the bill to the best of your ability
Record your measurement in the given section in your notes

3. Quantitative Observation
=measurements; must consist of two parts: a number and a unit
Ms. Ngo is 5’2”
Ms. Ngo is 52
What would happen if we did not have units??

4. Uncertainty
Any measurement involves an estimate and thus is uncertain to some extent

5. We saw this during the Do Now activity!
If 5 different people took a measurement of a pin, we could have 5 different measurements:
Person
Measurement 1
2.85 cm 2
2.84 cm 3
2.86 cm 4 5
We saw this during the Do Now activity!

6. Person Measurement 1 2.85 cm 2 2.84 cm 3 2.86 cm 4 5
If 5 different people took a measurement of a pin, we could have 5 different measurements:
The first two digits are the same regardless of who made the measurement (these are called certain numbers))
Person
Measurement 1
2.85 cm 2
2.84 cm 3
2.86 cm 4 5

7. The last digit varies; it is called the uncertain number
If 5 different people took a measurement of a pin, we could have 5 different measurements:
The last digit varies; it is called the uncertain number
Person
Measurement 1
2.85 cm 2
2.84 cm 3
2.86 cm 4 5

8. Accuracy
Measure of how close a measurement comes to the actual/accepted value
Accepted Value = 24 cm
Measured Values
(Experimental Values)
Measurements
24.1 cm
24.0 cm
23.9 cm

9. Precision
Measure of how close a series of measurements are to one another
Measurements
88.7 in
88.8 in
88.9 in

10. Group Discussion
* *The more numbers the more precise the tool

11. Series of Measurements Can Be…

12. Think-Pair-Share…
Six students used this ruler to measure the metal strip shown. Their measurements are listed in the table.
In terms of accuracy and precision, how would you classify their measurements?

13. Review
Compare the precision of a 100 mL graduated cylinder with 1 mL increments with a 50 mL graduated cylinder with 0.5 mL increments.
A 50 mL graduated cylinder with 0.5 mL increments is more precise because the increments are smaller

14. Review
The chart below shows the volume of a solution measured by four different groups. The actual (correct) volume of the solution is 44.5 mL.
What group has both accurate and precise data?
Group 1
What group has data that is imprecise and inaccurate?
Group 2
Comment on the accuracy and precision of Group 3’s data?
Their data is precise and inaccurate.
Volume (mL)
Group 1
Group 2
Group 3
Trial 1
44.5 mL
42.3 mL
49.0 mL
Trial 2
44.6 mL
47.2 mL
49.1 mL
Trial 3
48.0 mL

15. Review
To determine the length of a running shoe, a cross-country runner measured the shoe several times using a metric ruler. If the true length of the shoe is 88.74cm, give an example of:
imprecise and inaccurate data
precise but inaccurate data
precise and accurate data

16. Measuring Volume in the Lab
Volume is measured from the bottom of the meniscus

17. Take the Volume!
(Always take a measurement to the first uncertain number.)

18. Correct Answer:
56.0 mL

19. Take the Volume!
(Always take a measurement to the first uncertain number.)

20. To be correct, your answer must be in the following range:mL

21. |Experimental-Accepted|
Percent Error
Used to gage how close an measurement taken via experiment is to the accepted value
|Experimental-Accepted|
Accepted Value
% Error =
Do not have to memorize formula; It’s located on last page of Reference Table

22. Significant Figures in Measurement
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit

23. Counting Significant Figures
Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
m ___
Complete this sentence: All non-zero digits in a measured number are
(significant or not significant). 3 5

24. Leading Zeros 0.008 mm 1 0.0156 oz 3 0.0042 lb ____ 0.000262 mL ____
Number of Significant Figures
0.008 mm 1
oz 3
lb ____
mL ____
Complete this sentence : Leading zeros in decimal numbers are
(significant or not significant). 2 3

25. Sandwiched Zeros Number of Significant Figures 50.8 mm 3 2001 min 4
0.702 lb ____
m ____
Complete: Zeros between nonzero numbers are (significant or not significant). 3 3

26. Trailing Zeros
Number of Significant Figures 25,000 in yr 1 48,600 gal 3 25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders. 5

27. Learning Check 1) 22.0 and 22.00 2) 400.0 and 40
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and 150,000

28. Learning Check
State the number of significant figures in each of the following:
A m
B L
C g
D m
E. 2,080,000 bees

29. Learning Check
A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) x 103 2) ) C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105 4 3 3

30. Independent Practice Worksheet Work alone or with a partner
Perfect time for questions

31. Significant Figures in Calculations & Rounding
Unit 1: Measurement & Matter

32. Rounding w/ Sig Figs COMPUTE answer first!!!!
CHOOSE whether to round based on sig figs or decimal places

33. CALCULATION RULES For Multiplication & Division
limiting term = one w/ the SMALLEST # of sig figs

34. Multiplication & Division
CALCULATION RULES
Multiplication & Division
Round answer to the same number of sig figs as the answer with the fewest sig figs

35. 6.4 Example 6.384 4.56 x 1.4 = Round to 3 sig figs 2 sig figs

36. Example
3.702
Round to 4
x 3 =
4 sig figs
1 sig fig
1 sig fig

37. CALCULATION RULES For Addition & Subtraction
limiting term = one w/ the smallest number of DECIMAL PLACES

38. Addition & Subtraction
CALCULATION RULES
Addition & Subtraction
Round answer to the same number of decimal places as the measurement with the fewest decimal places

39. Significant Figures in Calculations=
Round to
15.28
15.281
3 decimal places
2 decimal places
2 decimal places

40. Significant Figures in Calculations=
Round to 10
9.8
1 decimal place
0 decimal places
0 decimal places

41. Summary Only as precise as your “weakest link”
The one w/ fewest sigs figs/decimal places
Multiplication/ Division-> sigs figs
Addition/Subtraction -> decimal places

42. You Try….
2.45 x 3.5
8.315 ÷ 298
135 x 246 x x x 155
3.6x10-3 x
8.6
0.0279
286
0.029 or 2.9x10-2

43. You Try… = =
1081 – 7.25 =
8.445 x 105 – 9.44 x 102 =
31.1
55.69
1074
8.44 x 105