1. Making Measurements and Using Numbers
The guide to lab calculations

2. Not just numbers
Scientists express values that are obtained in the lab. In the lab we use balances, thermometers and graduated cylinders to record mass, temperature and volume. It may seem simple to read the instruments but it is actually more difficult than you think.

3. Reading Thermometers Thermometers measure temperature. Key points:
Temperature is read from the bottom to top.
Lines on a thermometer are only so accurate. We as scientist are allowed to estimate between the lines.
The unit on thermometers is Celsius

5. Estimating Lines
We are allowed to estimate one additional digit to make the reading more significant.
No matter what the last line of reading may be on the measuring device being used, you may estimate one additional digit (with a few exceptions)

6. Estimation Tips
When markings go up or down by ones, estimate your measurement to the tenths place
When markings go up or down by tenths, estimate your measurement to the hundreths place
When markings go up or down by 2 ones or 2 tenths, estimate your measurement to that place

7. Why do we estimate lines?
Some errors or uncertainty always exists in measurements. The measuring instruments place limitations on precision.
When using a device we can be almost certain of a particular number or digit. Simply leaving the estimated digit out would be misleading because we do have some indication of the value’s likely range.

8. Reading Liquid Volume
Because of certain physical properties, liquids are attracted or repelled from glass surfaces. Water is especially attracted to glass. Due to this attraction a meniscus forms when water is in glass tubing.
Meniscus is the upside down bubble that forms when water is in glass

9. When reading glass volumes, the volume is of liquid is read at the bottom of the meniscus.
Not only is the liquid read at the bottom of the meniscus but the last digit of the reading is estimated.
The estimation tips are the same for all measuring devices
No matter the guess you are right. As long as you include the guess in your answer

10. Water Meniscus

11. Significant figures
In science, measured values are reported in terms of significant figures.
Significant Figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

12. Why Use Sig Figs? We can only measure as well as our equipment
We cannot make estimates without being precise
Estimating multiple measurements can add up to a lot of error

15. Insignificant digits may still be recorded if they act as placeholders.
Scientist don’t write down all the numbers the calculator displays.
To determine if a value is significant the following rules are applied:

16. Rule 1 All non-zero numbers are significant. Examples:
123 L has 3 significant figures (sigfigs)
7.896 m3 has 4 sig figs
8 meters has 1 sig figs

17. Practice #1 Determine how many sig figs are in the following numbers:
885 mL Km
96 g

18. Rule 2 Zeros appearing between non zero digits are significant.
Examples:
40.7 L has 3 sig figs
87,009 km has 5 sig figs

19. Practice #2 Determine how many sig figs are in the following numbers:
305 sec
mol
molecules

20. Rule 3
Zeros appearing in front of all non zero digits are not significant.
These zeros are place holders
Examples
m has 5 sig figs
kg has 1 sig fig

21. Practice #3 Determine how many sig figs are in the following numbers:
atm mm
psi

22. Rule 4
Zeros at the end of a number AND to the right of a decimal point are significant.
Examples
85.00 g has 4 sig figs
mm has 10 sig figs
L has 4 sig figs

23. Practice #4 Determine how many sig figs are in the following numbers:cm kg
mol

24. Rule 5
Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just a placeholder, it is not significant. A decimal point placed after zeros indicates they are significant
Examples
2000 m has only 1 sig fig
2000. M has 4 sig fig (decimal at the end)

25. Practice #5 Determine how many sig figs are in the following numbers:Hz

26. Why Do Insignificant Figures Need To Sometimes Be Recorded?
Insignificant figures may still be recorded if they act as placeholders to keep the value of how large or small the number is credible.
5000 m only has 1 sig fig but we still need to keep the 3 zeros as placeholders

27. Cumulative Practice #1
Determine how many sig figs are in the following numbers:
385 sec J
ft cal
6.0 mm in L yd mL

28. When To Apply Sig Fig Rules?
Sig fig rules only apply to situations where a measurement was made by an instrument.
For all other situations, all measurements are exact, and therefore contain an unlimited amount of significant figures.
300 mL = 1 sig fig
300 people = 3 sig figs
300 pennies = 3 sig figs

29. Cumulative Practice #2
Determine how many sig figs are in the following numbers:
400 sheep
400 mg of C12H22O11
lbs
80 bananas

30. Rounding With Sig Figs
Round each of the following calculations to 3 significant figures:
~ ~ 1010
~ ~ 54600
Look at the number following the 3rd sig fig to determine rounding
If this number is _ 5, round 3rd sig fig up
If this number is < 5, keep 3rd sig fig the same
>

31. Calculations with Sig Figs
When multiplying and dividing, limit and round to the the number with the fewest sig figs.
5.4 x 17.2 x =
1.500 / x =

32. When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer = =

33. Units
For calculations involving multiplication, add exponents of units if the same
Ex: cm1 x cm1 x cm1 = cm3
For calculations involving division, subtract exponents of units if the same
Ex: cm3 / cm2 = cm1 or cm
For calculations involving adding or subtracting, exponents must be the same
Ex: cm + cm + cm = cm

34. Practice Working With Units
m2 - m2 =
m3 / m2 =
mm + mm + mm =
mm x mm x mm =

35. Scientific notation
Scientist often deal with very small and very large numbers, which can lead to a lot of confusion about counting zeros.
Scientist notation takes the from of
M x 10n where 1 <M<10 and “n” represents the number of decimal places moved.

36. How Are Sig Figs Applied To Numbers In Scientific Notation?
M x 10n -All numbers included in the “M” factor are ALWAYS significant -All numbers included in “n” are NEVER significant

37. becomes 1.5 x 105
becomes 4.35 x 107
becomes 3.4 x 10-3
becomes x 10-12

38. Scientific Notation Practice
Write the following in scientific notation or in standard form, given the following:
6.350 x 102
4.7 x 10-2

39. Multiplying & Dividing Using Scientific Notation
Ex: (4.58 x 105) (6.8 x 10-3)
Multiply the bases x 6.8 =
Add the exponents = 102
Adjust value to correct scientific notation format x  x 103
Determine sig figs from quantities listed in the original problem x 103

40. Ex: (2.8 x 10-5) / (3.673 x 10-2)
Divide the bases 2.8 / =
Subtract the exponents = 10-3
Adjust value to correct scientific notation format x10-3  x 10-4
Determine sig figs from quantities listed in the original problem 7.6 x 10-4

41. Adding & Subtracting Using Scientific Notation
Ex: (3.52 x 106) + (5.9 x 105) – (6.447 x 104)
Convert all quantities so that they all have the same largest exponent
(3.52 x 106) + (.59 x 106) - ( x 106)
Add or subtract the base numbers
= x 106
Adjust value to correct scientific notation format
x 106
Determine sig figs from quantities listed when all exponents have been adjusted. (red)
4.05 x 106

42. Practice Calculations With Scientific Notation
(7.36 x 102) + (2.9 x 10-2) =
(3 x 102) x (2.9 x 10-1) =
(1.20 x 102) / (5.000 x 105) =

43. Accuracy vs. Precision
Accuracy is the ability of a tool or technique to measure close to the accepted value of the quantity being measured (how close it is to being right)
Precision is the ability of a tool or technique to measure in a consistent way (how close the measurements are to each other)

45. Example Problem
A student measured a magnesium strip 3 times and recorded the following measurements: 5.49cm, 5.48cm, 5.50cm
The actual length of the strip is 5.98cm. Describe the results in terms of accuracy and precision.

46. Density Density is a mass to volume ratio D = m/v m = Dv v = m/D
Density is an intensive property and will not change regardless of the amount of matter present.
Each substance has its own defined density value ex. H2O = 1g/cm3

47. How Can Density Be Determined In The Lab?
You must know the mass and volume if you want to experimentally determine the density of a sample of matter
Mass can be found using a scale (g)
Volume can be found by one of two ways:
For regular shaped objects, use a ruler to find
l x w x h (measurement will be in cm3)
For irregular shaped objects, use water displacement (measurement will be in mL)

48. Remember… 1cm3 = 1mL
Water displacement is a process in which an object is submerged in water. The difference between the water level before and after the object is submerged in the water will be the volume of the object

49. Example Problems
A sample of metal has a mass of g and a volume of 45.0 cm3. What is the density of this metal?
What is the volume of of a piece of zinc with a mass of g? DZn= 7.14 g/mL

50. The water level in a graduated cylinder stands at 13
The water level in a graduated cylinder stands at 13.5 mL before a copper sample is lowered into the cylinder. The water level then rises to 19.8 mL after the sample is submerged. What is the mass of this sample? DCu = 8.92 g/cm3

51. Percent Error… How Wrong Are You?
Once your densities are determined experimentally, you can then compare your lab results to the theoretical value by using the following equation:
% error = (theoretical – experimental)
theoretical
X 100
Ideally, you would shoot for <5% error in any lab experiment
Theoretical values are given by teacher or text

52. Remember…
Theoretical values are definitive. These values will be given by the teacher or can be found in a published source (textbook).
Experimental results are always found in the lab.

53. Example Problem After calculating the density of ethanol as
.801 g/mL in the lab, you want to see how well you performed. Would Mrs. Rustad be happy with these results? Why or why not? Dethanol = .791 g/mL