Metric Conversions Through dimensional analysis The Metric System

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.

1000 n 10 n Prefix Symbol Short scale Long scale Decimal equivalent in SI writing style 10008 1024 yotta Y Septillion Quadrillion 1 000 000 10007 1021 zetta Z Sextillion Trilliard (thousand trillion) 1 000 000 10006 1018 exa E Quintillion Trillion 1 000 000 000 10005 1015 peta P Quadrillion Billiard (thousand billion) 1 000 000 000 10004 1012 tera T Trillion Billion 1 000 000 10003 109 giga G Billion Milliard (thousand million) 1 000 000 10002 106 mega M Million 10001 103 kilo k Thousand - 102 hecto h Hundred 100 - 101 deca, deka da Ten 10 10000 100 (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) 1000− 3 10− 9 nano n Billionth Milliardth 0. 000 001 1000− 4 10− 12 pico p Trillionth Billionth 0. 000 000 001 1000− 5 10− 15 femto f Quadrillionth Billiardth 0. 000 000 001 1000− 6 10− 18 atto a Quintillionth Trillionth 0. 000 000 000 001 1000− 7 10− 21 zepto z Sextillionth Trilliardth 0. 000 000 000 001 1000− 8 10− 24 yocto y Septillionth Quadrillionth 0. 000 000 001 Millionth 1 000 001

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

Conversion Factors Conversion factor 109 Large 106 3 10 prefix 102 101 Base units (L, m, g, s) = (L, m, g, s) = Prefix 1 giga (G) 1 mega (M) 1 kilo (k) 1 hecto (h) 1 deca (da) NEED TO MEMORIZE Base units (L, m, g, s) Small prefix Base units 1 (L, m, g, s) = 1 (L, m, g, s) = Conversion factor 101 102 103 106 109 1012 Write These Down! (Take NOTE of the CASE) Prefix deci (d) centi (c) milli (m) micro (μ) nano (n) pico (p)

CONVERSION STEPS 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 1* NO NAKED NUMBERS!!! EVERY NUMBER* NEEDS A UNIT!!! NO UNIT = WRONG ANSWER!!!

STEP 3: Copy given unit downstairs to cancel 2. 43 m m 1 m STEP 4: Put the unit you are looking for on top mm 2. 43 m m 1 STEP 5: Put a 1 in front of larger unit: consult your chart! mm 2. 43 m 1 1 m THIS IS THE MOST IMPORTANT AND MISSED STEP

STEP 6: LOOK UP THE PREFIX FOR CONVERSION FACTOR 2. 43 m 103 mm 1 1 milli = 1000 or 103 m STEP 7: MULTIPLY ACROSS, NOT CROSS MULTIPLY 2. 43 m 103 mm 1 1 m = 2. 43 x 103 mm 1 STEP 8: Reduce and double check your unit 2. 43 E 3 1 = 2. 43 3 x 10 mm

Problem: Convert 561 liters (L) into kiloliters (k. L) 561 L 1 k. L 1 103 L = kilo 561 = 1000 k. L or 103 5. 61 1 Step 3 2 4 1 5 Step 867 E- k. L

Problem: Convert 4. 39 E 4 seconds (s) into nanoseconds (ns) 4. 39 E 4 s 1 109 ns 1 s = E 13 ns 4. 39 nano = 109 1 4. 39 E 13 Step 3 2 4 1 5 Step 867 ns

Problem: Convert 93561 grams (g) into Megagrams (Mg) 93561 g 1 1 106 Mg g = 93561 Mega = 106 Mg 6 10 9. 36 Step 3 2 4 1 5 Step 867 E-2 Mg Mg

PRACTICE 1) 2) 3) 4) 3. 45 Ms to s 1000 m to hm 356 L to p. L 7 1. 54 x 10 g to Gg

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

2. 55 km to cm 2. 55 km 103 m 1 1 km 102 cm = 1 m 2. 55 x 103 x 102 cm = 1 x 1 x 1 2. 55 x 105 cm

1. 63 E 3 cg to Mg 1. 63 E 3 cg 1 1 g 1 Mg = 102 cg 106 g 1. 63 E 3 Mg 2 6 x 10 1 x 10 = 1. 63 x 10 -5 Mg

PRACTICE 1) 3. 45 Ms to ms 2) 1000 nm to hm 3) 356 m. L to p. L 4) 1. 54 x 107 cg to Gg

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

Answers: 1 -5 table conversion 6. 91 m 1 9. 10 E 12 m 1 1. 8932 E 6 mm 1 100 cm 1 m 6. 91 E 2 cm 9. 10 E 3 Gm 1. 89 E 3 m 1 Gm 9 10 m 1 m 3 10 mm

231 cm 1 94 km 1 1 m 2 10 cm 103 m 1 km 2. 31 m 9. 40 E 4 m

A C E 1 m 1 m 1 km 100 cm 3 10 m G 1 Gm 9 10 m I K 9 10 nm 1 Mm 1 m 6 10 m

F D 3 10 mm 100 cm 1 km 1 m 1 m L J B H 6 10 m 1 m 9 10 m 1 Mm 9 10 nm 1 Gm

Meter Stick 1 meter 10 1 1 1 1 1 decimeter decimeter decimeter 10 1 1 1 centimeter centimeter 1 1 decimeter centimeter 1 1 centimeter 10 1 1 millimeter 1 1 1 centimeter millimeter 1 1 millimeter

Fractions : Ratios Q: How do you convert a number into a fraction? Ex: 2. 57 1 A: Put the number over 1!