1. Scientific Measurements

2. BIG NUMBERS Scientists often work with very large numbers.
National debt = $5,653,000,000,000
Bill Gates' net worth = $75,030,000,000
Distance to Alpha Centauri = 40,120,000,000,000,000 m
Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g
Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,000 g

3. Scientists often work with very small numbers.
Radius of hydrogen atom = m
Mass of Hydrogen atom = g
Mass of electron = g

4. What to do?
Scientific notation – way of expressing a value as the product of a number between 1 and 10 and a power of 10.

5. Examples 300,000,000 Move the decimal 8 places to the left = 3 x 108
750,000
Move the decimal 5 places to the left
= 7.5 x 105

6. More Practice
230,000,000
2.3 x 108
40,000
4 x 104
34,000,000
3.4 x 107

7. Scientific Notation cont.
Scientific notation can also be used to write out very small numbers.
0.0005
Move the decimal 4 places to the right
5 x 10-4

8. More Practice
= 2 x 10-6
0.0045
= 4.5 x 10-3
= 7.5 x 10-5

9. Practice - Reverse 3 x 103 4 x 106 3.4 x 105 2.0 x 104 = 3,000
= 4,000,000
= 340,000
= 20,000

10. More Practice 6 x 10-5 4.5 x 10-2 3.5 x 10-3 5.5 x 10-7 = 0.00006
= 0.045 = =

11. Reliability in Measurements
Precise measurements will give the same results again and again
Accuracy is how close you are to the accepted value

12. Where would you measure?

14. Certainty in Measurement
Significant digits are those digits that are certain in your measurement plus one estimated
In order to count significant digits just count the digits
5.6
781
6,778
What about large or small numbers?

15. BIG NUMBERS Scientists often work with very large numbers.
National debt = $5,653,000,000,000
Bill Gates' net worth = $57,030,000,000
Distance to Alpha Centauri = 40,120,000,000,000,000 m
Distance to Andromeda Galaxy = 21,800,000,000,000,000,000,000 g
Mass of Sun = 1,990,000,000,000,000,000,000,000,000,000,000 g

16. Scientists often work with very small numbers.
Radius of hydrogen atom = m
Mass of Hydrogen atom = g
Mass of electron = g

17. Atlantic Pacific Rule
If decimal is Absent starting from the right count all digits after the 1st non zero
If decimal is Present starting from the left count all digits after the 1st non zero

18. Practice 4500 Liters 0.00543 grams 0.00607000 seconds 500,003 meters
400,000. Joules
Amps

19. Exact Numbers
Remember that the rules of Sig Figs only apply to measurements and not exact numbers.
Years in a century
Students in a classroom
Centimeters in a meter

20. Rounding Sig Figs Remember to keep the value of the number the same.
Remember to round up if last digit is 5 or more.
Round 12.5 to 2 sig figs
Round kg to 3 sig figs
Round mL to 4 sig figs
Round 303 meters to 3 sig figs
Round 303 meters to 2 sig figs

21. Multiplying / Dividing SigFigs
When multiplying/dividing measurements you are limited by the measurement with the least number of significant digits.

22. Practice Area = L x W Length = 6.15 m Width = 4.026 m
Volume = L x W x H
Volume = 3.05 x 2.10 x 0.75

24. SI Units SI units: a revised form of the metric system
SI base units are fundamental units all other units are based upon

25. Base Units Physical Quantity Name of SI unit Symbol for SI unit length
meter m
mass
kilogram kg
time
second s
electric current
ampere A
temperature
Kelvin K
amount of substance
mole
mol
luminous intensity
candela cd

26. Derived units Derived units are made from a combination of base units.
Examples:
Volume
Density

27. Examples of SI derived units expressed in terms of base units
Derived quantity
SI derived unit
Name
Symbol
area
square metre m2
volume
cubic metre m3
speed, velocity
metre per second
m/s
acceleration
metre per second squared
m/s2
wavenumber
1 per metre
m-1
density, mass density
kilogram per cubic metre
kg/m3
specific volume
cubic metre per kilogram
m3/kg
current density
ampere per square metre
A/m2
magnetic field strength
ampere per metre
A/m

28. Converting Metric Units
SI units based upon factors of 10
Begin with the prefix given and move the decimal the same number and direction to the desired prefix
Know the prefixes and values: The ones most important for us are Kilo (1,000), Centi (.01) and Milli (.001) Others can be looked up as needed or will be given in the problem.

29. Practice A soda can holds 355 mL convert to L Convert 76 km to meters
Convert 18 mm to cm
A Thumb drive holds 512 Megabytes convert to Kilobytes
Violet Light has a wavelength of 430 nm convert to km

30. Ratios Ratios are a common way of expressing results in Chemistry
Teacher to student ratio
Velocity
Population Density
Density
Ratios of chemicals in a chemical reaction

31. Finding Density Density = Mass / Volume Units are (kg/m3) or (g/mL)
Lets calculate Density
Mass = 27 kg
Volume = 3.0 mL
Denstiy = 9.0 kg/mL

32. More Practice
Mass = 45 kg
Volume = ???? mL
Density = 5.0 kg/mL

33. Practice Mass = 10.0 g Volume of water only = 35.0 mL
Volume of water w/ Object = 40.0 mL
Volume of object only = __________
Density = ______________

34. Practice
An aquarium has dimensions of 25.0 cm by 68.5 cm by 34.0 cm. If the mass of the aquarium if 2.3 kg, calculate the density.
The density of air is g/cm3 . How much mass does air have in a volume of 400. cm3?

35. Water & Density Water has a density of 1.0 g/ml at 4o C
Water’s mass in grams is equal to its volume in mL
Any object with a density greater will sink. . . less will float
1cm3 = 1cc = 1ml

36. Percent error
There is always some error in your measurement It is unavoidable. To calculate use the following formula: % Error = ((measured value – accepted value)/ accepted value ) X 100 % or % error = ((O - A)/A ) X 100 % PERCENT ERROR CAN BE NEGATIVE !!! In Science, a negative percent error means your value was less than the accepted value. This is very common in Chemistry.

37. Practice
When measuring the density of gold you find a value of 20.9 g/cm3 . The accepted value is 19.3 g/cm3. What is your error ?
Samantha S. Sloppiness measured the volume of her soda before she drank it for her midmorning snack. She measured the volume of the 12 oz. bottle to be 10 oz. What is her error ?

38. Answers
# 1 ((20.9 – 19.3) / 19.3 ) x 100 % = %
Notice it is a positive number since the answer was more than the real value.
# 2 ((10 – 12) / 12 ) x 100 % = %
Notice it is a negative number since the answer was less than the real value.