Dimensional Analysis CONVERTING UNITS

The Fundamental SI Units (ie: Système International, SI) Physical Quantity Name Abbreviation Mass kilogram kg Length meter m Time second s Temperature Kelvin K Amount of Substance (1 mol = 6.02x1023) mole mol

BASE UNIT SI Prefix Abbr Exp Meaning Equality mega M 106 kilo k 103 1 million x larger 1,000,000 base unit = 1 M_ kilo k 103 1,000 times larger 1,000 base unit = 1 k_ deca da 10 10 times larger 10 base unit = 1 D_ BASE UNIT (meters, grams, liters, etc.) 1 1 base unit deci d 10-1 1/10 1 base unit = 10 d_ centi c 10-2 1/100 1 base unit = 100 c_ milli m 10-3 1/1,000 1 base unit = 1,000 m_ micro  10-6 1/million 1 base unit = 1,000,000 _ nano n 10-9 1/billion 1,000,000,000 n_ pico p 10-12 1/trillion 1,000,000,000,000 p_

Y Z E P T G M k h da d c m µ n p f a z y FACTOR ...or in full ... or in words SI PREFIX SI SYMBOL 1,0E+24 1,0E+21 1,0E+18 1,0E+15 1,0E+12 1,0E+9 1,0E+6 1,0E+3 1,0E+2 1,0E+1 1,0E-1 1,0E-2 1,0E-3 1,0E-6 1,0E-9 1,0E-12 1,0E-15 1,0E-18 1,0E-21 1,0E-24 1 000 000 000 000 000 000 000 000 1 000 000 000 000 000 000 000 1 000 000 000 000 000 000 1 000 000 000 000 000 1 000 000 000 000 1 000 000 000 1 000 000 1 000 100 10 0,1 0,01 0,001 0,000 001 0,000 000 001 0,000 000 000 001 0,000 000 000 000 001 0,000 000 000 000 000 001 0,000 000 000 000 000 000 001 0,000 000 000 000 000 000 000 001 septillion sextillion quintillion quadrillion trillion billion million thousand hundred ten tenth hundredth thousandth millionth billionth trillionth quadrillionth quintillionth sextillionth septillionth yotta- zetta- exa- peta- tera- giga- mega- kilo- hecto- deca- deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto- Y Z E P T G M k h da d c m µ n p f a z y

SI Basic Units & Quantities Length = meter (m) Volume = volume of 1m x 1m x 1m cube = 1 m3 More convenient = liter (L) 1 cm3 = 1 mL 10 drops H2O ≈ 1 mL Mass = kilogram (kg) Defined as the mass of 1 L of H2O @ 4ºC weight is a force that measures the pull on a given mass by gravity

SI Basic Units & Quantities Temperature = Celsius (°C) - Water freezes @ 0 °C Water boils @ 100 °C Kelvin (K) - the absolute scale Don’t use the degree symbol Water freezes @ 273 K Water boils @ 373 K K = °C + 273 °C = K - 273

Conversion Factors Quantities can be expressed several different ways 1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies 1 meter = 10 decimeters = 100 centimeters = 1000 millimeters Conversion Factor: a ratio of equivalent measurements Units are vital Numerator and denominator are equivalent Conversion factors change the number & unit, however, the actual size of the quantity measured remains the same.

Conversion Factors Examples: 1 dollar = 100 pennies 1 dollar 1 L = 1,000 mL 1 L 1,000 mL OR 1,000 mL 1 L

Conversion Factors Smaller # Larger Unit 1 dollar 100 pennies Larger # Smaller Unit How many significant figures does a conversion factor within a system of measurement have? Unlimited

Dimensional Analysis 60 min 1 h 60 sec 1 min 8 h x x = 28,800 s Set up conversion factors so that the units will cancel out to get to the desired unit Cancel units & check for correct units Multiply by numbers on the top Divide by numbers on the bottom

Dimensional Analysis A way to analyze and solve problems using units, or dimensions, of the measurements. How many seconds are in a workday that lasts exactly eight hours? Unknowns Knowns Plan Solve

Dimensional Analysis How many seconds are in a workday that lasts exactly eight hours? Unknowns 8 hours = ? seconds Knowns time worked = 8 hours 1 hour = 60 minutes 1 minute = 60 secondsseconds Plan - use the units Solve

Dimensional Analysis 60 min 1 h 60 sec 1 min 8 h x x = 28,800 s Set up conversion factors so that the units will cancel out to get to the desired unit Cancel units & check for correct units Multiply by numbers on the top Divide by numbers on the bottom

Converting meters to centimeters 135 meters is how many centimeters? Unknown= ? cm = 135 meters Known: 1 meter = 100 cm Plan: m  cm Solve: 135 m x 100 cm = 1 m ** Multiple top values, divide bottom values. 13, 500 cm

Converting meters to centimeters 233 centimeters is how many meters? Unknown= ? m = 233 centimeters Known: 1 meter = 100 cm Plan: cm  m Solve: 233 cm x 1 m = 100cm ** Multiple top values, divide bottom values. 2.33 m

Converting meters to centimeters 233 centimeters is how many millimeters? Unknown= ? mm = 233 centimeters Known: 1 centimeter = 10 mm Plan: cm  mm Solve: 233 cm x 10 mm = 1 cm ** Multiple top values, divide bottom values. 2330 mm

Converting meters to centimeters 3456 millimeters is how many centimeters? Unknown= ? cm = 3456 millimeters Known: 1 centimeter = 10 mm Plan: mm  cm Solve: 3456 mm x 1 cm = 10mm ** Multiple top values, divide bottom values. 345.6 cm

Convert the Following 99.2 cm to meters Unknown: Known: Plan: Solve:

Convert the Following 2.34 m to cm Unknown: Known: Plan: Solve:

Convert the Following 2340 mm to cm Unknown: Known: Plan: Solve:

How many eggs do YOU weigh? What is your unknown? What do you know? What is your plan? Solve the problem!! ? = 5 dozen eggs weigh 2.5 kg

How many eggs do YOU weigh? = What is your unknown? What do you know? What is your plan? Solve the problem!! 5 dozen eggs weigh 2.5 kg

Convert the Following How many minutes are there in exactly one week?

Convert the Following How many seconds are in exactly a 40-hour work week?

Convert the Following 0.044 km to meters

Convert the Following 15 cm3 to liters

Convert the Following The radius of a potassium atom is 0.227 nm. Express this radius in the unit centimeters.

Convert the Following The diameter of the Earth is 1.3 x 104 km. What is the diameter expressed in decimeters?

U: K: P: S:

Convert the Following The mass of a unit volume of a substance is a property called density. The density of manganese is 7.21 g/cm3. What is the density of manganese expressed in units kg/m3?

Convert the Following Gold has a density of 19.3 g/cm3. What is the density in kilograms per cubic meter?