1. Measurements
Number followed by a Unit from a measuring device
SI Units (Le Système international d'unités) – based on the metric system
Time second (s)
Length meter (m)
Mass kilogram (kg)
Temperature Kelvin (K)
Amount of a substance mole (mol)

2. Metric Prefixes

3. What is Scientific Notation?
Scientific notation is a way of expressing really big numbers or really small numbers.
It is most often used in “scientific” calculations where the analysis must be very precise.
For very large and very small numbers, scientific notation is more concise.

4. Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 1 0 x

5. Conversion factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units
Dimensional Analysis (Factor-label method)
A way of solving problems using conversion factors
By using dimensional analysis the UNITS ensure that you have the conversion factor in the proper arrangement

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

7. Which of the two clocks below has the potential to be the most accurate? Why?

8. Comparing Rulers

9. Zero as a Measured Number Last (estimated) digit is 5.00 cm
. l I I I I cm
What is the length of the line?
First digit ?? cm
Second digit ? cm
Last (estimated) digit is cm

10. Reading a Meterstick
. l I I I I cm
First digit (known) = ?? cm
Second digit (known) = ? cm
Third digit (estimated) between
Length reported = 2.75 cm
or 2.74 cm
or 2.76 cm

11. Rules for Significant Figures
adapted from Russo's Reliable Rules for Significant Figures
All non-zero digits are significant
Zeroes between non-zero digits are significant
In measurements containing an expressed decimal, zeros to the right of NON-ZERO digits are significant.

12. “Atlantic - Pacific Rule”
Count from the ocean towards the coast starting with the first nonzero digit, and include all the digits that follow.

13. Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing

14. Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
Practice:
2.45 cm cm cm
18.92 mL mL
g -13 g g
14.6 cm
8.50 mL
12 g

15. Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.
Practice:
4.20 m x m x m
g / mL
(3.28 x 10-5 km) / (4 x 102 s)
2.2 m3
1.11 g/mL
8 x 10-8 km/s

16. Temperature Scales Fahrenheit Celsius Kelvin Anders Celsius 1701-1744
Lord Kelvin
(William Thomson)

17. Temperature Scales Kelvin Celsius 373 K 100 ˚C 100 K 100˚C 273 K 0 ˚C
Boiling point of water
373 K
273 K
100 K
100 ˚C
0 ˚C
100˚C
Freezing point of water
Notice that 1 kelvin = 1 degree Celsius

18. K = ˚C + 273 Calculations Using Temperature
Generally require temp’s in Kelvin
K = ˚C
Body temp = 37 ˚C = 310 K
Liquid nitrogen = ˚C = 77 K

19. Derived Units – a combination of 2 or more base units
Area (length x length)
Speed (length per time)
Volume (length x length x length)
Density (mass per volume)

20. DENSITY
Aluminum
Platinum
Mercury
13.6 g/cm3
21.5 g/cm3
2.7 g/cm3

21. Volume Displacement 25 mL
A solid displaces a matching volume of water when the solid is placed in water.
33 mL
25 mL

22. Learning Check
What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm3 2) 6 g/cm3 3) 252 g/cm3

23. Solution
Volume (mL) of water displaced = 33 mL - 25 mL = 8 mL Volume of metal (cm3) = 8 mL x 1 cm3 = 8 cm3 1 mL Density of metal = mass = 48 g = 6 g/cm3 volume 8 cm3

24. Can you hit the bull's-eye?
Three targets with three arrows each to shoot.
How do they compare?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
Can you define accuracy and precision?

25. How can someone show the accurate the measurement?
Calculation of percent error
(Value accepted - Value experimental)
Value accepted
Percent Error (%) =
x 100

26. Graphing Data Bar graphs Circle graphs Line graphs
Directly proportional
Inverse proportional