1. Ch 2 Measurement

2. Metric Mishap caused loss of NASA orbiter
On 9/23/99, $125,000,000 Mars Climate Mars’ atmosphere 100 km lower than planned and was destroyed by heat.
NASA lost a Mars orbiter because one team used metric units for a calculation and the other team didn’t. This mishap caused the loss of $125 million dollars!

3. Metric Jokes
1 million microphones = 1 megaphone 2000 mockingbirds = two kilomockingbirds 10 cards = 1 decacards graham crackers = 1 pound cake 10 millipedes = 1 centipede

4. orld have agreed on a single
SI System
orld have agreed on a single
Scientists all over the world have agreed on a single measurement system called Le Systeme International d’Unites
Based on powers of ten

6. Derived SI UNITS

7. Density can help identify substances

8. Volume is the amount of space an object occupies
The derived SI unit is cubic meters m3
The cubic centimeter is also used
The Liter, L, is a non-SI unit
1L = 1000cm3
1ml = 1cm3

9. SI Base Units of Measurement

10. Mass is a measure of the quantity of matter the Kilogram is the standard unit of mass
Weight is a measure of the gravitational pull on matter
Mass does not depend on gravity

11. Metric Prefixes

12. Conversion factors
Conversion factors are made from any two terms that describe the same or equivalent “amounts” of what we are interested in.
For example, we know that:
1 inch = centimeters
1 dozen = 12
12 inches OR foot
1 foot inches
1 dozen = 12
1 dozen or
dozen

13. (The equality that looks like a fraction)
Example Problem #1
How many feet are in 60 inches? Solve using dimensional analysis.
All dimensional analysis problems are set up the same way. They follow this same pattern:
What units you have x What units you want = What units you want
What units you have
The number & units you start with
The units you want to end with
The conversion factor
(The equality that looks like a fraction)

14. Example Problem #1 (cont)
You need a conversion factor. Something that will change inches into feet.
Remember
12 inches = 1 foot
Written as an “equality” or “ratio” it looks like
60 inches
5 feet x =
(Mathematically all you do is: 60 x 1  12 = 5)
What units you have x What units you want = What units you want
What units you have

15. dimensional analysis can be used for conversion of a single unit or a series of units.
Example Problem~ A snail crawls at a speed of 12 cm/min. How fast does a snail crawl in km/ hr? Note that the snail’s speed isn’t going to change; you are simply expressing it in different units cm x 1 m x 1 km x 60 min = km min cm m hr hr NOTE: Only multiplication and division are required.

16. Example Problem #1 (cont)
The previous problem can also be written to look like this:
60 inches 1 foot = 5 feet
12 inches
This format is more visually integrated, more bridge like, and is more appropriate for working with factors. In this format, the horizontal bar means “divide,” and the vertical bars mean “multiply”.

17. Example Problem
You need to put gas in the car. Let's assume that gasoline costs $3.35 per gallon and you've got a twenty dollar bill. How many gallons of gas can you get with that twenty? Try it!
$ gallon = gallons
$ 3.35
(Mathematically all you do is: 20 x 1  3.35 = 5.97)

18. Example Problem #4 (cont)
$ gallon 24 miles 1 day week
$ gallon miles 7 days
= weeks
(Mathematically : 20 x 1  3.35 x 24  1 x 1  7.1 x 1  7 = 2.88 )

19. Steps:
Given quantity w/its unit
Set up conversion factor
Place given unit as the denominator of the conversion factor
Place desired unit as the numerator
Place a “1” in front of the large unit
Find how many power of tens the smaller unit is
Cancel Units – only the desired unit should be left
Solve the problem
An aspirin tablet contains 325 mg of active ingredient. How much is this in cg?
325 mg
1 cg
= = 32.5 cg 1
10 mg 10
= 32.5cg of active ingredient

20. Metric Prefixes

21. Convert cubic units and squared units.
To convert from one unit of volume to another unit of volume, always use the conversion factor three times. To convert from one unit of area to another, use the conversion factor two times. Convert 15,800,000 mm3 to cm3. 15,800,00 mm3 x 13 cm3 = 103 mm3 Convert 2,700 mm2 to m2 2,700 mm2 x 12 m2 = (1000)2 mm2

22. Conversions involving 2 units
Convert one unit at a time and make sure to cancel units Convert 55 miles to km hour min