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Metric Conversions! Through dimensional analysis.

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Uses SI units ( Système International d’Unités) Universal standard of measurement used in science, and most of the rest of the world Based on factors of 10 The Metric System

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ENGLISH SYSTEM Ounces, Pounds and Pints 8 ounces make a cup, 2 cups make a pint, 2 pints make a quart, 4 quarts make a gallon. A pint of water weighs a pound. An American barrel of dry measure is 105 dry quarts (116 liters), but a liquid barrel is 31.5 gallons (liquid) or 119 liters, unless the barrel contains petroleum, in which case it contains 42 (US) gallons or 159 liters. The three different ounces: a fluid ounce is ml a troy ounce is 31.1 g an ounce avoirdupois is g There's also something called "dry measure" with units of pint, quart, peck and bushel for measuring quantities of fruits, grains, and whatnot. 1 pint dry is l, while 1 pint liquid is l. Inches, Rods, Chains and Furlongs An inch is the outer part of a man's thumb, 25.4 millimeter to be exact. 12 inches to a foot, 2 feet to a cubit or 3 feet to a yard. A rod/pole is 5.5 yards (16.5 feet): The size of a big stick carried around by builders (hence the name). Four rods make a chain (22 yards) - the distance between two (cricket) wickets. Ten chains make a furlong. A furlong square is ten acres. Eight furlongs make a mile. ?

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Choose the correct measurement for the job. Instead of saying an object traveled 5,000 meters you can reduce that to 5 kilometers 1 kilometer = 1000 meters Number Economy

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SI prefixes 1000 n 10 n PrefixSymbolShort scaleLong scaleDecimal equivalent in SI writing style yottaYSeptillionQuadrillion zettaZSextillionTrilliard (thousand trillion) exaEQuintillionTrillion petaPQuadrillionBilliard (thousand billion) teraTTrillionBillion gigaGBillionMilliard (thousand million) megaMMillion kilokThousand hectohHundred deca, dekadaTen (none) One1 -10 −1 decidTenth −2 centicHundredth −1 10 −3 millimThousandth −2 10 −6 microµ (u)Millionth −3 10 −9 nanonBillionthMilliardth −4 10 −12 picopTrillionthBillionth −5 10 −15 femtofQuadrillionthBilliardth −6 10 −18 attoaQuintillionthTrillionth −7 10 −21 zeptozSextillionthTrilliardth −8 10 −24 yoctoySeptillionthQuadrillionth

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Time Temperature Distance Mass Volume Measuring Instruments Second (s) Celcius ( o C), Kelvin (K) Meter (m) Gram (g) Liter (L), cm 3

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Prefix Conversion Factors 10 9 (L,m,g,s) =1 giga (G) 10 6 (L,m,g,s) = 1 mega (M) 10 3 (L,m,g,s) = 1 kilo (k) 10 2 (L,m,g,s) =1 hecto (h) 10 1 (L,m,g,s) = 1 deca (da) Base units (L, m, g, s) 1 (L,m,g,s) =10 1 deci (d) 1 (L,m,g,s) = 10 2 centi (c) 1 (L,m,g,s) = 10 3 milli (m) 1 (L,m,g,s) = 10 6 micro (μ) 1 (L,m,g,s) = 10 9 nano (n) 1 (L,m,g,s) =10 12 pico (p) Small units Large units NEED TO MEMORIZE Write These Down! (Take NOTE of the CASE) Base units Conversion factor Base units Conversion factor Prefix

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1 CONVERSION STEPS STEP 1: Draw your table Problem: convert 2.43 meters (m) into millimeters (mm) STEP 2: Put given number and unit over m NO NAKED NUMBERS!!! EVERY NUMBER NEEDS A UNIT!!! NO UNIT = WRONG ANSWER!!!

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1 STEP 3: Put given unit downstairs to cancel 2.43 m 1 STEP 4: Put the unit you are looking for on top 2.43 m m m mm STEP 5: Put a 1 in front of larger unit: consult your chart ! m m mm 1 THIS IS THE MOST IMPORTANT AND MISSED STEP m

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1 STEP 6: LOOK UP THE PREFIX FOR CONVERSION FACTOR STEP 7: MULTIPLY ACROSS, NOT CROSS MULTIPLY 2.43 m m mm STEP 8: Reduce and double check your unit 1 = mm m m mm 1 1 milli = 1000 or = 2.43 E3 1 mm

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Step 2 Step 3 Step 6 Step 1 Step 4 Step 5 kL L L kL1 kilo = 1000 or E-1 Problem: Convert 561 liters (L) into kiloliters (kL) kL = Step 7 Step 8

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4.39 E13 ns Step 2 Step 3 Step 6 Step 1 Step 4 Step 5 ns E4 s s ns 10 9 nano = E13 Problem: Convert 4.39 E4 seconds (s) into nanoseconds (ns) 1 = Step 7 Step 8

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93561 Mg Step 2 Step 3 Step 6 Step 1 Step 4 Step 5 Mg g g Mg1 Mega = E - 2 Problem: Convert grams (g) into Megagrams (Mg) 10 6 = Step 7 Step 8

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Ms to s m to hm L to pL x 10 7 g to Gg PRACTICE

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You have to convert to the base unit first How do you know? Problem has 2 prefixes and no base unit alone Example: km to cm, Mg to mg, mL to GL 2 Stage Problems Convert to m first Convert to g first Convert to L first (L, m, g, s)

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x 10 3 x 10 2 cm km km to cm km m 1m cm 1 = 1 x 1 x 1 = 2.55 x 10 5 cm

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E3 Mg E3 cg E3 cg to Mg cg g 10 2 g Mg 10 6 = 1 x 10 2 x 10 6 = 1.63 x Mg

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Ms to ms nm to hm mL to pL x 10 7 cg to Gg PRACTICE

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6.91m 1 1m 100 cm 6.91 E2 cm 9.10 E12 m m 1 Gm 9.10 E3 Gm E6 mm mm 1 m 1.89 E3 m Answers: 1-5 table conversion

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231 cm cm 1 m 2.31 m 94 km 1 1 km 10 3 m 9.40 E4 m

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1Mm 10 6 m 10 9 nm 1m 1Gm 10 9 m 1m 100cm 1m 10 3 mm 1km 10 3 m AC E GI K

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10 3 mm 1m 10 9 nm B DF 10 9 m 1Gm HJ 10 6 m 1Mm L 100cm 1m 10 3 m 1km

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1millimeter1millimeter 1centimeter1centimeter1centimeter Meter Stick 1 meter 1decimeter1decimeter1decimeter1decimeter1decimeter1decimeter1decimeter1decimeter1decimeter 1decimeter 1 decimeter 1 centimeter 1centimeter1centimeter1centimeter1centimeter1centimeter 1centimeter 1centimeter 1millimeter1millimeter1millimeter1millimeter1millimeter1millimeter1millimeter1millimeter

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Q: How do you convert a number into a fraction? Ex: 2.57 A: Put the number over 1! Fractions : Ratios 1

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