Units, Conversions & Dimensional Analysis
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- It is useful to have an idea of the physical meaning of
- For example, there are 86,400 seconds in a day. If you
had to recount the 443,912 votes cast in Broward County, FL in November
2002, how long would it take you if you could parse votes at one per
- You want to rent storage space. How big exactly is 27
cubic feet? Is the space big enough to store your 30 year old Carmengia
notation saves writing. Positive exponents (first
two examples) are numbers greater than one, whereas negative exponents
are numbers between zero and one.
- 5.382x1012 = 5,382,000,000,000 -
to the right of the five.
- 5.382x1011 = 538,200,000,000 -
to the right of the five.
- 5.382x10-6 = 0.000005382 - the
number is less
than one, write the five at the sixth place to the right the decimal.
- It is VERY helpful to know your
prefixes and what
- tera - trillion - 1012 =
- giga - billion - 109 =
- mega - million - 106 = 1,000,000
- kilo - thousand - 103 = 1,000
- centi - hundredth - 10-2 = 1/100
- milli - thousandth - 10-3 =
- micro - millionth - 10-6 =
- nano - billionth - 10-9 =
- pico - trillionth - 10-12 =
figures determine how precise a measurement is.
- If you have a stick that is known to be one meter long
demarcations, is this a good tool to measure fractions of a meter? You
measure a distance to be 10 meter sticks long, and then some. Is it
meaningful to add the quantity 3cm to this distance? Why or why not?
- Rules of significant figures
- Leading zeroes are not significant
- 0.0017 has two significant figures
- Trailing zeroes are not significant if they are needed
to hold a place
- 1700 has two significant figures
- 0.001700 has four
significant figures - there is implied precision in writing the extra
- Zeroes within a number are significant
- 0.0107 has three significant figures
- 1205 has four significant figures
- If you wish to ensure all digits of a whole number are
significant, add a decimal point:
- 127,000. has six significant figures whereas 127,000
only has three
- Things you should know about units
- Everyone but US uses the metric system. It's easier.
you rather answer: how many teaspoons are in a gallon or how many
milliliters are in a liter?
- Life is easier if you work with like units. For example,
you are working with distances, decide whether to use kilometers,
miles, feet, meters, etc...Pick a unit and stick with it! If you are
working with time, choose whether it's better to use minutes, seconds,
hours, days, etc...
- As you learn new things in this class, you will need
their units. Almost every quality we talk about will have a unit. Learn
it up front, like you would vocabulary in your English class, and you
will be much happier.
- Converting units (an example)
- Convert 3.1 miles into kilometers.
First Know the conversion factor.
These are in your
book in the back cover. In this case 1 mi = 1.609 km.
Second Determine what the final unit
you need is. In
this case, we want kilometers. Thus we want to write our conversion
factor as a ratio with kilometers on top:
Third Set up a table and do the math
Finally divide out the common units
(in this case
mi) from the top and bottom answers on the right [so mi*km/mi = km],
and divide the top number 4.9879 by the bottom number 1 [4.9879/1 =
4.9879] and put the two together to get the answer: 4.9879 km.
- Dimensional Analysis is the use of units to validate a
formula or result. For example: