1. Meas

2. Do you know how to take a measurement?

3. Do you know how to work with the measurements you take?

4. Chapter 2
Significant Digits

5. Taking Measurements All measurements involve one estimation.
If the measuring device is digital it will take the estimation for you.

6. Electronic Measuring Devices
Digital readout measuring diameter of inches.
The last zero is the estimated digit.

7. Taking Measurements All measurements involve one estimation.
If the measuring device is scaled you must take the estimation yourself.

8. Scaled Measuring Devices

9. Scaled Measuring Devices
Use the bottom ruler to measure the length of the metal bar.

10. Scaled Measuring Devices
Bottom ruler gives a measurement of 8.? cm.

11. The Importance of Units
The Mars Climate Orbiter was launched by NASA in December 1998 at a cost of $125 million dollars.
The orbiter was to go into orbit around Mars on Sept. 23rd 1999.

12. The Importance of Units
It entered Mars atmosphere 100 km (62 miles) lower than it was supposed to and was destroyed.
The loss of the satellite cost not only millions of dollars and lost time but was because of a simple problem that all high school science students should understand.

13. The Importance of Units
Different groups of scientists failed to include units on calculations and therefore mixed English units with SI units.

14. The Importance of Units
Engineers who built the spacecraft specified thrust in pounds, which is an English unit. Scientists who launched the satellite assumed the thrust was calculated in the metric unit newtons.
But since the units were not specified the mistake was not caught until it was too late.

16. Scaled Measuring Devices
Measure the length of the metal using the top ruler.

17. Measuring Volume
When liquid is put into a container, a meniscus can form which can cause error in reading the measurement
A meniscus is the curved surface of liquid in a narrow cylindrical container
So how do we read the meniscus?

18. How to read a meniscus.
Read the meniscus at the bottom of the curved surface
Avoid parallax error: when a measurement is read at an angle rather than straight at eye level .

19. How to read a meniscus. ml

20. Read the Volume in mL

21. Measuring Temperature
When measuring the temperature of a liquid, it is important to not allow the bottom of the thermometer touch the walls or bottom of the container the liquid is in
Measuring the temperature is similar to that of measuring volume.

22. What is the temperature?

23. Measuring Mass When using the balance it is important to:
Measure using a weigh boat rather than just putting something directly on the pan
Do not measure hot or cold objects (can warp the balance)
Always check that the balance is zeroed.
Clean up any spilled chemicals around the balance

24. How would I measure this mass?

25. Significant Digits

26. Rules for Significant Digits
All non-zero digits are significant.
96 g. 2 significant digits
61.42 g. 4 significant digits
0.538 g. 3 significant digits

27. 2. “Trailing” zeros after the decimal point ARE significant.
s. 6 significant digits
s. 4 significant digits
0.002 m. 1 significant digits

28. 3. Zeros between significant digits are significant.
5.029 km. 4 significant digits
30600 km. 3 significant digits
km. 5 significant digits

29. All other zeros are NOT significant unless indicated to be so by having a bar placed over them._
10 mL 2 significant digits
1000 mL 1 significant digit
mL 4 significant digits

30. How to Determine Significant Digits
Underline the leftmost nonzero digit.
Use the rules for significant digits to determine the rightmost significant digit.
Every digit in between the leftmost and rightmost significant digits are significant as well.

31. Counting or Exact Numbers
Counting numbers: If there are 10 people in a room there are not 9.5 or people in the room. Counting numbers are exact.
Ones in Conversion Factors: 1 kilometer = 1000 meters.  Exactly 1 km is equal to exactly 1000m. The 1 is considered to be an exact number and so is the 1000.
Since Counting numbers and metric conversions are exact they have an infinite number of significant digits.

32. Determine the Significant Digits
70.12 L mg µm
27.0 km
50 people
1.002 cm
200 kg ºC
1000 mL
42, cm
225 beans dm m
3,200,000 µL

33. Determine the Significant Digits (Examples in Notebook)
mg 3
µm 5
27.0 km
50 people infinite
1.002 cm
200 kg ºC
1000 mL
42, cm
225 beans infinite dm m
3,200,000 µL

34. Math Operations with Significant Digits
When multiplying and/or dividing your answer must reflect the smallest number of significant digits.

35. Math Operations with Significant Digits
When multiplying and/or dividing your answer must reflect the smallest number of significant digits.
(17.3 cm)(28 cm) = cm2

36. Math Operations with Significant Digits
When multiplying and/or dividing your answer must reflect the smallest number of significant digits.
(17.3 cm)(28 cm) = cm2 = 480 cm2

37. Math Operations with Significant Digits
When multiplying and/or dividing your answer must reflect the smallest number of significant digits.
(17.3 cm)(28 cm) = cm2 = 480 cm2
708g ÷ 4.700ml = g/ml =

38. Math Operations with Significant Digits
When multiplying and/or dividing your answer must reflect the smallest number of significant digits from the numbers being multiplied/divided.
(17.3 cm)(28 cm) = cm2 = 480 cm2
708g ÷ 4.700ml = g/ml = 151g/ml

39. Addition and/or Subtraction reflects the fewest decimal places from the numbers being added/subtracted.
24.6 cm − cm = 7.59 cm

40. Addition and/or Subtraction reflects the fewest decimal places.
24.6 cm − cm = 7.59 cm = 7.6 cm

41. Addition and/or Subtraction reflects the fewest decimal places.
24.6 cm − cm = 7.59 cm = 7.6 cm
8.5g g g =

42. Addition and/or Subtraction reflects the fewest decimal places.
24.6 cm − cm = 7.59 cm = 7.6 cm
8.5g g g = 10g

43. Addition and/or Subtraction reflects the fewest decimal places.
24.6 cm − cm = 7.59 cm = 7.6 cm
8.5g g g = 10g = 10.0g

44. Are Significant Figures Important?
A student was given an assignment and a budget of $50 to complete it.
Assignment: Get a cube of metal which has a mass of 83 grams.
He knew the density of the metal was 8.6 g/mL, and used this to calculate the cube's volume.

45. Are Significant Figures Important?
Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the volume of the cube to be about mL.

46. Are Significant Figures Important?
He then calculated that the edge of the cube had to be cm. He took his plans to the machine shop where his friend had the same type of work done the previous year.
The shop foreman said, "Yes, we can make the cube according to your specifications."

47. Are Significant Figures Important?
He knew his friend had paid $35 for a similar metal cube, and he had been given $50 out of the school's research budget to get the job done so he assumed that he would have plenty of money.

48. Are Significant Figures Important?
He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still working on it. Try next week."
Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case.

49. Are Significant Figures Important?
Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill.

50. Are Significant Figures Important?
"$500, and cheap at the price. We had a difficult job getting it right -- had to make three before we got one right."

51. Are Significant Figures Important?
"But--but--my friend paid only $35 for the same thing!"
"No. He wanted a cube 2.1 cm on an edge, and your specifications called for 2.129cm.

52. Are Significant Figures Important?
We had yours roughed out to 2.1 cm the day that you brought it in.
However it was the precision grinding and lapping to get it to the cm specifications which took so long and cost the big money.