1. Dimensions & Unit Conversions
August 16, 2016
Working in table groups, write down the table below. Then, find 3 different quantities to measure. This means 3 different TYPES of measurements (for example, weight and length are different quantities). Take your measurement in SI units. Write the measurements on your white board, filling in just the first two columns.
Quantity Measurement Dimension Units SI or not?
10 minutes to do, then discuss (5 minutes)
Looking for the students to find 3 physical quantities (dimensions): time, length, and mass.
Possible misconceptions: they might measure angles, which are not exactly a quantity (they are dimensionless). They measure weight (which is not metric and is a quantity but is a derived quantity)

2. In Table Groups …
Find 3 different quantities to measure. This means 3 different TYPES of measurements (for example, weight and length are different quantities). Take your measurement in SI units.
For now, fill in only the first two columns on your GN 

3. Dimensions & Units
All physical quantities have dimensions and are expressed in units.
Dimension describes what the physical quantity is
Units are how the quantity is measured
Example: Speed
Speed has the dimensions of Length / Time
Speed may be measured by a variety of different units
(e.g. mph, km/s, etc.)
You can convert between different units of the same physical quantity (e.g. seconds into hours) but CANNOT convert one dimension into another (e.g you can’t convert time into length)

4. The corresponding basic SI- units are:
In the study of mechanics, we will work with physical quantities that can be described in terms of three dimensions:
length (L), time (T) , and mass (M).
The corresponding basic SI- units are:
Length – 1 meter (1m) is the distance traveled by the light in a vacuum during a time of 1/299,792,458 second.
Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sevres, France
Time – 1 second (1s) is defined as 9,192,631,770 times the period of oscillation of radiation from the cesium atom.
These standards (definitions) have obviously evolved over time. Earlier standards were simpler but less reproducible (e.g. a gram was mass of cubic cm of water).

5. ALL physical dimensions can be expressed in terms of combinations of seven basic dimensions, which can be measured directly.
Derived dimensions are combinations of 7 basic ones.
Basic
Physical
Quantity
Derived
Physical
Quantity
Basic
Dimension
Basic
SI Unit
Derived
Dimension
Derived
SI Unit
Distance, height,width
Length (L)
meter (m)
Mass (m)
Mass (M)
kilogram (kg)
Time (t)
Time (T)
second (s)
Electric Current (I)
Electric
Current (I)
ampere (A)
Temperature
kelvin (K)
Amount of matter
mole
Intensity of light
candela (cd)
area L2 m2
Volume L3 m3
speed
L/T
m/s
acceleration
L/T2
m/s2
force
ML/T2
kg.m/s2
newton (N)
power
M L2/T3
kg.m2/s3
watt (W)
density
M/ L3
kg/m3
Blue ones are ones we will work with this semester – start learning them, but do not need to memorize by next class

6. Go back to the measurements you did earlier
& fill in the rest of the table
Quantity measured
Measurement
Dimensions
Units
SI or not?

7. They are grouped into steps 10± 3
base unit 1
femto pico nano micro mili kilo mega giga tera
f p n m m k M G T
centi deci
c d
Smaller units
Larger units
every step is 10± 1 power
They are grouped into steps 10± 3

8. SI conversions! 1 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 c d
f p n m m k M G T
c d
SI conversions!
larger unit →
smaller number
The problem: We have to convert 5 into kl.
Will the number in front of kl be smaller or bigger?
Smaller!!
5 𝑚ℓ=_______ 𝑘ℓ

9. Because sometimes moving the decimal won’t work … more on this later!1
f p n m m k M G T
Moving the decimal seems so much easier … why do we bother with conversion factors?
Because sometimes moving the decimal won’t work … more on this later!
c d
SI conversions!
larger unit →
smaller number
We can do SI unit conversions in two different methods:
5 𝑚ℓ=_______ 𝑘ℓ
= 1
5 𝑚ℓ=5 𝑚ℓ× 1𝑘ℓ 𝑚ℓ =5× 10 −6 𝑘ℓ
Method 1: Conversion factors
* Note: The larger unit always has a 1 in the conversion factor (i.e. 1 kℓ and 1 km).
5𝑚ℓ= 6 𝑠𝑡𝑒𝑝𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡 =5× 10 −6 𝑘ℓ
Method 2: Moving the decimal

10. Another problem! 1 10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 c d
f p n m m k M G T
c d
Another problem!
smaller unit →
bigger number
Will the number in front of cm be smaller or bigger?
larger!!
5 𝑘𝑚=_______ 𝑐𝑚
= 1
5 𝑘𝑚=5𝑘𝑚× 𝑐𝑚 1𝑘𝑚 =5× 𝑐𝑚
Method 1: Conversion factors
5𝑘𝑚= 5 𝑠𝑡𝑒𝑝𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡 𝑐𝑚 =5× 𝑐𝑚
Method 2: Moving the decimals

11. One more as a class … The wavelength of green light is 500 nm.
How many meters is this?
500 𝑛𝑚× 1𝑚 𝑛𝑚 =500× 10 −9 𝑚=5× 10 −7 𝑚 or
500 𝑛𝑚= 𝑚=5× 10 −7 𝑚

12. Practice using both methods on your whiteboard …
hold it up when you are done
I have 906 gigabyte hard drive on my computer.
How many bytes of data will it hold?
9.06 X 1010 bytes
Now practice more.
If you are confident, do them by yourself.
If you are not confident, then work with someone who is confident. BUT, the less confident one should be the one leading the practice and talking out their process!!!!

13. Practice 1: Basic SI conversions
How many liters is 16 𝜇ℓ ?
4.3 x 104 ns = ? µs
5.2 x 108 ms = ? ks
0.09 cm = ? pm
16 𝜇ℓ=1.6× 10 −5 ℓ
4.3× 𝑛𝑠 = 43 µs
5.2× 𝑚𝑠=520 𝑘𝑠
0.09 𝑐𝑚=9 𝑋 108 pm

14. When do you need to use conversion factors?
When converting between SI and English units
When converting between units that have exponents
Example 1: 20 m/s → km/h
Example 2: 7.2 m3 → mm3
20 𝑚 𝑠 = 20 𝑚 𝑠 1 𝑘𝑚 𝑚 𝑠 1 ℎ = 72 km/h
7.2 𝑚 3 =7.2 𝑚 𝑚𝑚 1 𝑚 3
= 7.2 x 𝑚𝑚 3

15. Let’s do two as a class … Problem 1: Problem 2: 100 mm3 → m3
100 𝑚𝑚 3 =100 𝑚𝑚 𝑚 𝑚𝑚 3
= 10-7 m3
60 mi/h = ? m/s
HINT: 1 mi = 1609 m
60 𝑚𝑖 ℎ =60 𝑚𝑖 ℎ 𝑘𝑚 1 𝑚𝑖 𝑚 1 𝑘𝑚 1 ℎ 3600 𝑠 = 27 m/s

16. Practice on your whiteboard … hold it up when you are done
75 𝑔 𝑐𝑚 2 =75 𝑔 𝑐𝑚 𝑘𝑔 𝑔 cm 1 m 2 = 750 kg/m2
75 g/cm2 → kg/m2
Now practice more (use homework)..
If you are confident, do them by yourself.
If you are not confident, then work with someone who is confident. BUT, the less confident one should be the one leading the practice and talking out their process!!!!

17. Closure What were our objectives today and how did we meet them?
How did what we do today reflect our statement of inquiry? … our TOK connection?
What was our learner profile trait, and how did we demonstrate it?

18. Exit Ticket 0.05 cm = _______ mm 9.3 X 105 nm = __________ mm
3.5 m / s = __________ km / hr
35 m2 = __________ km2
Bonus: What is the difference between systematic and random error?