Through dimensional analysis. Metric Conversions! Through dimensional analysis.

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

? 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 29.573 ml a troy ounce is 31.1 g an ounce avoirdupois is 28.35 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 0.551 l, while 1 pint liquid is 0.473 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. ?

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

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 1 000 000 000 000 000 000 000 000 10007 1021 zetta Z Sextillion Trilliard (thousand trillion) 1 000 000 000 000 000 000 000 10006 1018 exa E Quintillion Trillion 1 000 000 000 000 000 000 10005 1015 peta P Billiard (thousand billion) 1 000 000 000 000 000 10004 1012 tera T Billion 1 000 000 000 000 10003 109 giga G Milliard (thousand million) 1 000 000 000 10002 106 mega M Million 1 000 000 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 0.000 001 1000−3 10−9 nano n Billionth Milliardth 0.000 000 001 1000−4 10−12 pico p Trillionth 0.000 000 000 001 1000−5 10−15 femto f Quadrillionth Billiardth 0.000 000 000 000 001 1000−6 10−18 atto a Quintillionth 0.000 000 000 000 000 001 1000−7 10−21 zepto z Sextillionth Trilliardth 0.000 000 000 000 000 000 001 1000−8 10−24 yocto y Septillionth 0.000 000 000 000 000 000 000 001

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

Write These Down! (Take NOTE of the CASE) Conversion Factors Conversion factor Base units Prefix 109 (L,m,g,s) = 1 giga (G) 106 (L,m,g,s) = 1 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) = 101 deci (d) 1 (L,m,g,s) = 102 centi (c) 1 (L,m,g,s) = 103 milli (m) 1 (L,m,g,s) = 106 micro (μ) 1 (L,m,g,s) = 109 nano (n) 1 (L,m,g,s) = 1012 pico (p) Large units NEED TO MEMORIZE Base units Conversion factor Prefix Small units Write These Down! (Take NOTE of the CASE)

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

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

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

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

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

Step 3 Step 2 Step 4 Step 1 Step 5 Step 6 Step 7 Step 8 9.36 E-2 Mg Problem: Convert 93561 grams (g) into Megagrams (Mg) 93561 g 1 Mg 93561 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

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

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

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

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

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

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 1.8932 E6mm 1 m 1.89 E3 m 103 mm 1

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

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

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

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

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