Dimensional Analysis Look at title and pick apart. What does the word analysis mean? What word do you recognize in the word dimensional? What does it mean to have dimensions? 2D vs 3D?

Conversion Factors Ratio of equivalent measurements infinite number of sig. figs Written as fractions Reciprocals are also true Do you have change for my dollar in quarters? How many quarters would you have to give me?

Examples 4 quarters = 1 dollar 1 yd = 3 ft 4 quarters 1 dollar 1 yard 3 feet 3 feet 1 yard 1 yd = 3 ft

Metric Conversion Factors Property Base Unit Prefix Symbol Relationship Length meter (m) kilo k 1 km = 1000 m centi c 100 cm = 1 m milli m 1000 mm = 1 m nano n 109 nm = 1 m Mass kilogram (kg) 1 kg = 1000 g 1000 mg = 1 g Volume Liter (L) 1000 mL = 1 L micro mc or μ 106 μL = 1 L ** l mL = 1 cm3 (cubic centimeter or cc) 1 mg = 1000 mcg (microgram)

Problem solving steps Identify the given Draw your table Identify what your trying to find Find and insert conversion factors (cancel as you go) Multiply across numerators Divide by the denominators (individually) Round answer to “correct” sig figs (match the given measurement) DO NOT USE CONVERSION FACTORS WHEN CALCULATING SIG FIGS!!!!!!

Examples How many seconds old are you? Answer: 750,000 mg

How many teaspoons of Tylenol would a child take if the doctor prescribed 12 milliliters for their body weight? (1tsp = 5 mL) Answer: 2.4 tsp

If a bottle of Ibuprofen has 100 tablets and each tablet is 200 mg, how many micrograms are there in the bottle? Answer: 137.16 cm rounded to 140 cm

If a person drinks 2.00 liters of water per day, how many cups is that? (1 fl oz = 30mL, 1 cup = 8 fl oz) Answer 83.3