METRIC SYSTEM

Measuring Systems were confusing!!! Everyone used a different method!! We did not speak same language!! Could Not trade!!

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Developed Metric System French govt came up with it. Formed in 1799 Designed easiest system Simple Decimal based system All units divisible by 10 Called Système International d'Unités (or SI for short) SI

Who uses it??? Every country but US (and Myanmar and Liberia) US Slowly converting over to using it SCIENTISTS ALWAYS USE IT!!!

METRIC BASE UNITS Length = Meter, m Time = Seconds, sec Volume = liters, L Mass = grams, g Weight = Newtons, N

METRIC Prefixes Prefixes tell you how many of the base unit are present Examples: Kilo- means 1000 (kilometer literally means “1000 meters”) Centi- means 1/100 (one hundredth) (Centimeter literally means “1/100 of a meter”)

Metric System Giga- 1 billion base Mega- 1 million base Kilo – 1 thousand base Standard – base unit (meter, liter, etc) Deci – 1/10 th of base Centi – 1/100 th of base Milli – 1/1000 th of base Micro – 1 millionth of base Nano – 1 billionth of base

kilo1,000 hecto100 deca10 -- (base unit)unit-- deci0.1 centi0.01 milli0.001 Common Metric PrefixesUnit Multiples

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Convert these on your own… 5 m = ________________________cm 1300 mm = _______________________m 15 km = _________________________ m 12 km = _________________________ mm 270 cm = ________________________m cm = _______________________ km

How did you do??? 5 m = 500 cm 1300 mm = 1.3 m 15 km = 15,000 m 12 km = 12,000,000 mm 270 cm = 2.7 m cm = km

Memorize Conversion Factors 1000 meters in 1 kilometer 3600 seconds in 1 hour 1600 meters in 1 mile

METRIC REVIEW 32 cm = 0.32 m 762 mm = 0.762m 3.6 km = 3600m 63 ns = s 25 ms= s 350 km = 3.5 e 5 or 350, cm = m

0.432 mm = m or 4.32 e –4 400 g = 0.4 kg 16.9 mg = or 1.69 e –5 55 g = kg 5,000,000 mg= 5 kg 5275 g= kg g= 4.25 e –4 kg 4.25 mg= 4.25 e –6 kg

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Factor Label Method AKA : Dimensional Analysis

Why is factor label important? Factor label method allows us to solve problems that seem more difficult by breaking the problem down into parts. Factor label becomes very important when it is harder to convert quantities.

Important Ideas to Remember… The key to factor label is the cancellation of units. Always identify the known, unknown, and conversion factors in the problem. Only one number and one unit per box!!!!! Like units are always diagonal from one another. Unknown is placed in first column. The rest of the columns are conversion factors. m/s km/h mph are all fractional units!!! Important Conversion factors: 1000 meters in 1 km and 3600 seconds in 1 hour

Step One Determine your known, unknown, and the conversion factors needed. Known = what you start with in the problem, the given Unknown = what you are solving for, ? Conversion factors = memorized proportions or fractions that demonstrate how much of one unit is in another unit of measure. Ex: 12 eggs in a dozen. 3 ft in a yard m in a km….Etc…

Our Example… How many pumpkins are in 20 pumpkin patches, if there are 25 pumpkins in one pumpkin patch? Known = 20 pumpkin patches Unknown = pumpkins Conversion factors = 25 pumpkins 1 pumpkin patch

Step Two Set up the factor label “fence” = *** note  If using more than one conversion factor, you will need more fence posts***

Step Three Put Known with its units in first bracket. 20 pumpkin patches= One number and 1 unit per box!!!!!!

Step Four Place conversion factor in next bracket. Make sure when you use conversion factors, the known units are diagonal so you can cancel out the units that you want to eliminate. 20 pumpkin patches 25 pumpkins= 1 pumpkin patch Like units are always diagonal!!!

Step Five Multiply across the top. Multiply across the bottom. Cancel units. 20 pumpkin patches 25 pumpkins = 500 pumpkins 1 pumpkin patch1

See the cancellation? 20 pumpkin patches X 25 pumpkins = 500 pumpkins 1 pumpkin patch Like units have to be DIAGONAL!!

Step Six Divide the top (numerator) by the bottom (denominator) and answer the problem. 500 pumpkins = 500 pumpkins 1

Now try for yourself… How many centimeters are in 30 inches if there are 2.54 centimeters in one inch?

Were you right? Known = 30 inches Unknown = centimeters Conversion factor = 1 inch 2.54 cm 30 inches2.54 cm = 76.2 cm 1 inch1 There are 76.2 cm in 30 inches

Now try a more complicated problem… How many Kilometers are in 30,000 millimeters? There are 2 conversion factors Remember to use conversion factors. Even though we know we can just move decimal points, there is a bigger lesson to be learned!

Were you right? Known = 30,000 mm Unknown = Kilometers Conversion factors = 1000mm 1000 m 1 m 1 Km 30,000 mm 1 m 1 Km = 0.03 Km 1000 mm 1000 m There are 0.03 Km in 30,000 mm Like units are always diagonal

The most complicated problem… How many Km/h are in 15 m/s? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

Were you right? Known = 15 m/s Unknown = km/h Conversion factors = 1000m 3600 s 1 km 1 h = Remember: only one number and unit per block Like units have to be diagonal!! 15 m 1 s 1 km 1000 m 3600 s 1 h km 1000 h 15 m 1 s = 54 km/h

The most complicated problem… How many Km/h are in 30 m/s? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

Were you right? Known = 30 m/s Unknown = km/h Conversion factors = 1000m 3600 s 1 km 1 h 30 m 1 km 3600 s = 108,000 Km 1 s 1000 m 1 h 1000 h Answer: 108 km/h Remember: Like units have to be diagonal!!

The most complicated problem… How many m/s are in 30 km/h? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

Were you right? Known = 30 km/h Unknown = m/s Conversion factors = 1000m 3600 s 1 km 1 h 30 km 1000 m 1 h = m 1 h 1 km 3600 s 3600 s Answer: 8.3 m/s Remember: Like units have to be diagonal!!

Important Ideas to Remember… The key to factor label is the cancellation of units. Always identify the known, unknown, and conversion factors in the problem. Only one number and one unit per box!!!!! Like units are always diagonal from one another. Unknown is placed in first column. The rest of the columns are conversion factors. m/s km/h mph are all fractions!!!

Scientific Notation

Why is Scientific Notation Important??? Scientific notation makes it easier to work with very large numbers or very small numbers. Mass of earth = kg 6 x kg 6 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 kg

Scientific Notation on Your Calculator Most calculators now have a key on them for doing scientific notation. Look for one of the following... EXP (most Casio calculators) EE (most TI calculators, and you might have to use the 2nd function key to use it) 10x S.N. Do NOT use the "hat" symbol on your calculator to enter scientific notation (eg. 4.5 x 10^5). Your calculator will treat this as two separate numbers, and you will get some calculations wrong because of it (it screws up the proper order of operations).

Now try these…. Write 3,564,000 in scientific notation. Write in scientific notation. Remember only one number in front of the decimal point!!!

Were you right? X X 10 -3

Scientific Notation 5.0 x 10 –3 2.5 x x x x 10 –4 2.5 x x x x x 10 3

Standard Notation , ,

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Significant figures are those digits an experimenter records that he/she is sure of plus one very last digit that is doubtful Significant Figures

Sig Figs Examples: 1.78 m = 3 sig figs m = 4 sig figs 1500 m = 0 are not significant in this case, 2 sig figs 1502 m = 4 sig figs x 10 3 = 4 sig figs

Sig Figs When numbers are multiplied or divided, final answer has a sig fig equal to smallest number of sig figs in original factors In this class, we will not round until the very end of the problem. At the end, round to 2-3 decimal places.