1. Measurement & Calculations

2. Biblical Reference
He measured its wall and it was 144 cubits thick, by man's measurement, which the angel was using.
Revelation 21:17

3. Accuracy vs. Precision For a single measurement:
Accuracy - An indication of how close a measurement is to the accepted value
Precision - An indication of the degree of exactness of a measurement
For multiple measurements:
Accuracy - An indication of how close the average measurement is to the accepted value
Precision - An indication of the agreement among a number of similar measurements

4. Accuracy – measurement of closeness to the true value of a number

5. Precision – measure of how close a series of measurements are to one another

6. Scientific Notation: 602,000,000,000,000,000,000,000 copper atoms
6.02 x 1023 copper atoms
grams
3.27 x grams
Only 1 digit to the left of the decimal place.

7. Significant Figures:
When you make a measurement there is some estimation
Recorded numbers in a measurement or calculation are called significant figures
What is the length of the black line in cm?
How many significant figures are in the measurement?

8. Number of Significant Figures = 2
You can't always keep all the digits a calculator produces. You can only keep the significant ones, the ones that are not beyond the accuracy of the measuring device. These digits are called significant digits or figures.
Length cm
Number of Significant Figures = 2

9. Significant Figure Rules :
Non zeros count (123.34) – 5 Sig Figs
2. Leading zeros do NOT count (0.004) – 1 Sig Fig
3. Captive zeros count (2004, 2.004, 20.04) – 4 Sig Figs
4. Trailing zeros count IF there is a decimal point (20., 20.00, 0.200) – 2, 4, and 3 Sig Figs

10. Significant Figures in Calculations:
A calculated answer cannot be more precise than the least precise measurement from which it was calculated
Rounding
If the last number is less than 5, round down
If the last number is greater than 5, round up
If the last number is a 5, round so that the rounded number is even.

11. Mathematical Operations:
Rounding with Addition and Subtraction
Round to the least number of decimal places
Example: = 11.0
Rounding with Multiplication and Division
Round to the same number of significant figures as the measurement with the least number of significant figures
Example: 540. g / 62 ml = 8.7 g/ml

12. Determining Error:
Accepted value – correct value based on reliable references
Experimental value – value measured in lab
Error = Accepted Value – Experimental value
Percent Error = |Error| x 100
Accepted Value
*|Error| is the absolute value of the error

13. SI units Measurements are fundamental to the experimental sciences
Science uses the International System of Measurements (SI)
MKS and CGS

14. Measuring with SI Units - MKS
Quantity
SI Base Unit
Symbol
Length
meter m
Mass
kilogram kg
Temperature
Kelvin K
Time
second s
Amount of substance
mole
mol
Luminous intensity
candela cd
Electric current
ampere A

15. Metric Prefixes Prefix Meaning Factor mega (M)
1 million times larger than preceding
106
kilo (k)
1000 times larger than preceding
103
deci (d)
10 times smaller than preceding
10-1
centi (c)
100 times smaller than preceding
10-2
milli (m)
1000 times smaller than preceding
10-3
micro (m)
1 million times smaller than preceding
10-6
nano (n)
1 billion times smaller than preceding
10-9
pico (p)
1 trillion times smaller than preceding
10-12

16. Metric Units of Length Unit Relationship Example Kilometer (km)
1 km = 103 m
Five city blocks
Meter (m)
Base unit
Height of doorknob
Decimeter (dm)
101 dm = 1 m
Large orange
Centimeter (cm)
102 cm = 1 m
Shirt button
Millimeter (mm)
103 mm = 1 m
Thickness of dime
Micrometer (mm)
106 mm = 1 m
Diameter of bacteria
Nanometer (nm)
109 nm = 1 m
Thickness of RNA

18. Metric Units of Mass & Volume
Relationship
Example
Kilogram (kg)
1 kg = 103 g
Small textbook
Gram (g)
1 g = 10-3 kg
Dollar bill
Milligram (mg)
103 mg = 1 g
Sugar cube
Microgram (mg)
106 mg = 1 g
Single salt crystal
Unit
Relationship
Example
Liter (L)
Base unit
Quart of milk
Milliliter (mL)
103 mL = 1 L
20 water drops
Cubic centimeter (cm3)
1 cm3 = 1 mL
Sugar cube
Microliter (mL)
106 mL = 1 L
Single salt crystal

19. Standard Kilogram Height = 3.9 cm Diameter = 3.9 cm
Platinum-Iridium Cylinder

21. Metric Units of Temperature
The Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C.
The Kelvin scale sets 0 at absolute zero.
The units of Kelvin and Celsius are equivalent
K = °C
°C = K –

24. Metric Units of Energy 1 Joule (J)= 0.2390 calories (cal)
1 calorie (cal) = Joules (J)
One calorie is the amount of heat that raises the temperature of 1 g of pure water by 1 ° C

25. Derived Units

26. Derived Units

28. A conversion factor is a ratio that, when multiplied by the item you are converting, cancels out the units you do not want and leaves you with the units you want.
Dimensional Analysis is a technique where you use the dimensions/units to check if a relationship is correct.

29. Everyday Conversion Factors
1 dollar
4 quarters
10 dimes
20 nickels
100 pennies

30. Metric Conversion Factors
1 meter
10 decimeters 101
100 centimeters 102
1,000 millimeters 103
1,000,000 micrometers 106
1,000,000,000 nanometers 109

31. Conversion Factor Steps
Step 1 – Determine what units you are given and what units you need.
Step 2 – Determine what conversion factors you need to use.
Step 3 – Arrange the conversion factors so that the units you do not want cancel out.
Step 4 – Make sure your last unit is the unit need.

32. Conversion Examples 500 cm ´ 1 m = 5 m 100 cm 6 cm ´ 10 mm = 60 mm
8 h
60 min
60 sec =
28,800 s
1 h
1 min

33. Example Problem With sig figs
K2 is the world’s second tallest peak at 8000 m. What is the height of K2 in feet?
With sig figs

34. Dimensional Analysis Question
The period (T) of oscillation of a simple pendulum depends upon the acceleration of gravity(g) and the length (L) of the pendulum.
Which expression below represents the relationship between T, g and L?

35. Dimensional Analysis Question

36. Coordinate Systems - Cartesian

37. Coordinate Systems - Polar

38. Density Density = Mass / Volume
A cm3 sample of platinum has a density of 21.4 g/cm3. What is its mass?

39. Comparative Densities