Ch 2 Measurement

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!

Metric Jokes 1 million microphones = 1 megaphone 2000 mockingbirds = two kilomockingbirds 10 cards = 1 decacards 453.6 graham crackers = 1 pound cake 10 millipedes = 1 centipede

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 http://study.com/academy/lesson/english-system-of-measurement-definition-history-advantages-disadvantages.html

Derived SI UNITS

Density can help identify substances

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

SI Base Units of Measurement

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

Metric Prefixes

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 = 2.54 centimeters 1 dozen = 12 12 inches OR 1 foot 1 foot 12 inches 1 dozen = 12 1 dozen or 12 12 1 dozen

(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)

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

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. 12 cm x 1 m x 1 km x 60 min = 0.0072 km min 100cm 1000 m 1 hr hr NOTE: Only multiplication and division are required.

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”.

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! $ 20.00 1 gallon = 5.97 gallons $ 3.35 (Mathematically all you do is: 20 x 1  3.35 = 5.97)

Example Problem #4 (cont) $ 20.00 1 gallon 24 miles 1 day 1 week $ 3.35 1 gallon 7.1 miles 7 days = 2.88 weeks (Mathematically : 20 x 1  3.35 x 24  1 x 1  7.1 x 1  7 = 2.88 )

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 = 325 = 32.5 cg 1 10 mg 10 = 32.5cg of active ingredient

Metric Prefixes

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

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