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**Through dimensional analysis.**

Metric Conversions! Through dimensional analysis.

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**The Metric System 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

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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. **

Number Economy 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

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**Decimal equivalent in SI writing style**

SI prefixes 1000n 10n Prefix Symbol Short scale Long scale Decimal equivalent in SI writing style 10008 1024 yotta Y Septillion Quadrillion 10007 1021 zetta Z Sextillion Trilliard (thousand trillion) 10006 1018 exa E Quintillion Trillion 10005 1015 peta P Billiard (thousand billion) 10004 1012 tera T Billion 10003 109 giga G Milliard (thousand million) 10002 106 mega M Million 10001 103 kilo k Thousand 1 000 - 102 hecto h Hundred 100 101 deca, deka da Ten 10 10000 (none) One 1 10−1 deci d Tenth 0.1 10−2 centi c Hundredth 0.01 1000−1 10−3 milli m Thousandth 0.001 1000−2 10−6 micro µ (u) Millionth 1000−3 10−9 nano n Billionth Milliardth 1000−4 10−12 pico p Trillionth 1000−5 10−15 femto f Quadrillionth Billiardth 1000−6 10−18 atto a Quintillionth 1000−7 10−21 zepto z Sextillionth Trilliardth 1000−8 10−24 yocto y Septillionth

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**Measuring Instruments**

Time Temperature Distance Mass Volume Second (s) Celcius (oC), Kelvin (K) Meter (m) Gram (g) Liter (L), cm3

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**Write These Down! (Take NOTE of the CASE)**

Conversion Factors Conversion factor Base units Prefix 109 (L,m,g,s) = 1 giga (G) (L,m,g,s) = mega (M) 103 (L,m,g,s) = 1 kilo (k) 102 (L,m,g,s) = 1 hecto (h) 101 (L,m,g,s) = 1 deca (da) Base units (L, m, g, s) 1 (L,m,g,s) = deci (d) 1 (L,m,g,s) = centi (c) 1 (L,m,g,s) = milli (m) 1 (L,m,g,s) = micro (μ) 1 (L,m,g,s) = nano (n) 1 (L,m,g,s) = pico (p) Large units NEED TO MEMORIZE Base units Conversion factor Prefix Small units Write These Down! (Take NOTE of the CASE)

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**CONVERSION STEPS STEP 1: Draw your table**

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

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**THIS IS THE MOST IMPORTANT AND MISSED STEP**

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

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**2.43 E3 mm STEP 8: Reduce and double check your unit**

STEP 6: LOOK UP THE PREFIX FOR CONVERSION FACTOR 103 2.43 m mm milli = 1000 or 103 1 1 m STEP 7: MULTIPLY ACROSS, NOT CROSS MULTIPLY 103 2.43 m mm 2.43 E3 mm = 1 1 1 m STEP 8: Reduce and double check your unit 2.43 E3 2.43 E3 mm = 1

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**Step 3 Step 4 Step 2 Step 1 Step 5 Step 6 Step 7 Step 8 5.61 E-1 kL**

Problem: Convert 561 liters (L) into kiloliters (kL) 561 L 1 kL 561 kL 5.61 E-1 kL kilo = 1000 or 103 = 1 103 L 103 Step 3 Step 4 Step 2 Step 1 Step 5 Step 6 Step 7 Step 8

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**Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8 4.39 E13 ns 1**

Problem: Convert 4.39 E4 seconds (s) into nanoseconds (ns) 4.39 E4 s 109 ns 4.39 E13 ns 4.39 E13 ns nano = 109 = 1 1 s 1 Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8

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**Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8 9.36 E-2 Mg**

Problem: Convert grams (g) into Megagrams (Mg) g 1 Mg Mg 9.36 E-2 Mg Mega = 106 = 1 106 g 106 Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8

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PRACTICE 3.45 Ms to s 1000 m to hm 356 L to pL 1.54 x 107 g to Gg

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**2 Stage Problems 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 (L, m, g, s) Convert to m first Convert to g first Convert to L first

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**2.55 km to cm 2.55 km 103 m 102 cm = 1 1 km 1 m 2.55 x 103 x 102 cm =**

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**1.63 E3 cg to Mg 1.63E3 cg 1 g 1 Mg = 1 102 cg 106 g 1.63E3 Mg =**

1.63 x 10-5 Mg 1 x 102 x 106

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PRACTICE 3.45 Ms to ms 1000 nm to hm 356 mL to pL 1.54 x 107 cg to Gg

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**Answers: 1-5 table conversion**

6.91m 100 cm 6.91 E2cm 1 1m 9.10 E12m 1 Gm 9.10 E3 Gm 109 m 1 E6mm 1 m 1.89 E3 m 103 mm 1

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231 cm 1 m 2.31 m 102 cm 1 94 km 103 m 9.40 E4 m 1 km 1

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A C E 1m 100cm 1m 103mm 1km 103m G I K 1Gm 109m 109nm 1m 1Mm 106m

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F D B 103m 1km 103 mm 1m 100cm 1m L J H 106m 1Mm 1m 109nm 109m 1Gm

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**Meter Stick 10 10 10 1 meter 1 decimeter 1 centimeter 1 1 1 1 1 1 1 1**

millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 millimeter 1 centimeter

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

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