1. 2: Measurements and Calculations

2. Scientific notation
Used when dealing with very large or very small numbers
1 atom of gold = g
1g of H =602,000,000,000,000,000,000,000 atoms
300,000,000 m/sec =Speed of light
g = mass of a dust particle

3. How to Write in Scientific Notation
123,000,000,000  x
coefficient base exponent
Put the decimal after the first digit and drop the zeroes. The coefficient will be 1.23
The base is always 10
To find the exponent count the number of places from the decimal to the end of the number.

4. Scientific notation On your calculator:
Practice:
548,000,000,000
3.67 X 105
2.98 X 10-3
On your calculator:
Use EE or EXP button to mean “X 10”
2.98 X 10-3  2.98 EE -3
(2.98 X 10-3)(7.62 X 105) = ? ?=2271  2.27 X 103
2.45 X 10-9
5.48 X 1011
367000

5. Practice Convert to scientific notation Convert to standard notation
45700
0.0096
Convert to standard notation
4.5 x 10-5
2.1 x 104
6.33 x 108
2.98 x10-3

6. Measurement
No human endeavor can be called science if it cannot be demonstrated mathematically
Leonardo da Vinci ( )

7. Observations
Qualitative
Quantitative

8. SI (Système Internationaled’Unités) International System of Units
Base units
kg kilogram mass
m meter length
mol mole amount
s second time
K Kelvin temperature
A Ampere electric current
cd candela luminous
intensity

9. Derived SI Units m2 area m3 volume g/m3, g/cm3 density
J (Joule) energy
J = kg m2 s2

10. Non-SI Units L Liter Volume °C Celcius Temperature g/mL Density
atm atmosphere Pressure

11. Why use metric system? 98% world uses it
Used throughout scientific community
Easier- less memorizing
Uses powers of ten
Applies to all types measurements
What is the next smaller size wrench?
Powers of ten video

12. Metric Prefixes Used to make unit smaller or bigger mega M kilo k
deci d
centi c
milli m
micro 
nano n
pico p

13. Questions
If I went to the mall what unit would I use to measure the distance?
If I was measuring the length of a cell what unit would I use?
m, km, mm, cm, nm, m

14. Complete 1kg= ________g 1m= ________cm 1s= ________ps 1km= ________m
1g= ________ng
1cal= _______dcal
1m= _________m
1MJ = ________J
1L = _______mL

15. Metric Match Kg mg ms μg μm m Mg

17. Metric-U.S. Conversions
Need to know some metric-US relationships:
1 in = 2.54 cm
1 L = 1.06 quarts
1 kg = 2.2 lbs.

18. Volume measurements m3, cm3, dm3 L, mL 1L= 1000mL 1mL = 1cm3
Space something takes up
L x H x W
Units:
m3, cm3, dm3
L, mL
Know relationship
1L= 1000mL
1mL = 1cm3
1 sugar cube = 1cm3
20drops water = 1mL

19. Equipment used to measure volume

20. Mass Weight = force that measures the pull on a given mass by gravity
Mass = measure of the quantity of matter
SI unit is the Kilogram (Kg)

21. Temperature Temperature is a measure of heat transfer
Temperature Scales
Celsius (°C)
What is freezing point of water?
What is boiling point of water?
If it is 37 °C outside should you wear a sweater or a T-shirt?
Kelvin (K ) SI unit
A Kelvin is same size as a Celsius degree
Location of 0 is different

22. Temperature measurements

23. Conversion between Celsius and Kelvin
°C = K – 273 or K = °C + 273
Absolute Zero = 0 K What is this temperature in Celsius?
-273°C
Convert 25°C to K
298 K

24. How would you record the length of the nail?

25. Quantitative measurements
Numerical quantity
Appropriate unit
Uncertainty of the measurement

26. How would you record these volumes?

27. How would you record this volume?

28. Uncertainty in measurement
There is always some degree of uncertainty in any measurement
Why?
Measuring tool may have flaws
Always some estimation
involved when taking a
measurement

29. An object of ~54g is placed on three different balances

30.   
                                                                                                                                                      
All measurements have certain digits and one uncertain (estimated) digit

31. Significant Digits Measured digits in any measurement
Includes all certain digits and one estimated digit
Gives an indication of the accuracy of the instrument used for the measurement
Examples:
3.54 cm certain digits (3, 5)
1 uncertain digit (4)
3 significant digits
3.54 cm cm

32. Atlantic-Pacific Rules
Easy way to determine the number of significant digits in a measurement.
Pretend your
measurement is
the US

33. Atlantic The decimal point is absent in the number Atlantic – Absent
Start counting digits from atlantic side of the number.
Start counting at your 1st non-zero number
Example:
3 sig dig

34. Pacific The decimal point is present in the number Pacific – Present
Start counting digits from pacific side of the number.
Start counting at your 1st non-zero number
Example:
5 sig dig

35. How many significant digits?
2.640 X 10-3 cm Kg
6002
543 cars

36. Significant Digits in Calculations
Calculated value cannot reflect a greater accuracy than the initial measurements
Example:
I travel 59 miles in 3 hours. What is my speed?
59miles/3hrs = miles/hr
59miles/3hrs= 20miles/hr

37. Rounding
1. Determine the last sig dig your answer should have then round to that sig dig. Count from the left when determining last sig dig.
Look at the number immediately to the right of the last sig dig. If it is less than 5 it is dropped. If it is 5 or greater increase the last sig dig by one.
Examples
m (4sig dig)  314.7m
m (2 sig dig)  m
8792m (2 sig dig)  8800m

38. Addition/Subtraction
Answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places g g g
 g

39. Multiplication/Division
Round the answer to the same number of significant digits as the measurement with the least number of significant digits
(32.640m)(4.5 m) = m2  150m2

40. Practice 3419g + 3.912g + 7.0518g + 0.00013g = 145.63ml – 28.9ml =
20.8dm ÷123.1dm =
5.0cm x 5cm =
(3.68 x 106m)(1.64 x 10-8m) =
1.22 x 10-9m

42. Precision Accuracy Reproducibility
Standard deviation is measure or precision
Correctness
Percent error is measure of accuracy

43. Three groups of students measured the mass of a paper clip which had a known mass of 1.0004g.
Average g g
Which of the above sets of measurements are accurate
Which are precise
Which are precise and accurate
Which are neither precise nor accurate

44. % Error Error = accepted value – experimental value
% error = accepted value – experimental value x 100
accepted value

45. Example
A lab technician experimentally determined the boiling point of octane to be 124.1C. The actual boiling point of octane is 125.7C. Calculate the % error.
125.7ºC – 124.1ºC x 100 = 1.3%
125.7ºC

46. Density Ratio of the mass of an object to its volume
Density = mass g/ml or g/cm3
volume
Density is an intensive physical property that depends only on the composition of the substance,not on the size of the sample
The density of a substance usually decreasesas its temperature increases