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?

Definition Way to solve problems using the units, or dimensions, of the measurements

Conversion Factors Ratio of equivalent measurements Do not count when determining sig. figs. In chemistry we write them as fractions The reciprocal is 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 Length Unit Relationship Kilometer (km) 1 km = 1000 m Meter base unit Centimeter(cm) 100 cm = 1 m Millimeter (mm) 1000 mm = 1 m Mass Unit Relationship Kilogram (kg) base unit Gram (g) 1 kg = 1000 g Milligram(mg) 100 cm = 1 m

Volume Unit Relationship Kiloliter (kL) Liter (L) Milliliter (mL) base unit Milliliter (mL) 1000 mL = 1 L Cubic Centimeter(cm3) 1 cm3 = 1 mL

Problem solving steps Identify the given Draw your table Identify the finish line Find and insert conversion factors Multiply across numerators Divide by the denominators (individually) Round answer to correct sig figs! DO NOT USE CONVERSION FACTORS WHEN CALCULATING SIG FIGS!!!!!!

Examples How milligrams are in 750 grams. (1 g = 1000 mg) Answer: 750,000 mg

How many kilograms are in 10.5 grams. (1kg=1000 g) Answer: 0.0105 kg

How many milligrams would a 0. 75 lb. hamburger weigh. (1 lb = 453 How many milligrams would a 0.75 lb. hamburger weigh? (1 lb = 453.6 g, 1000 mg = 1 g) Answer: 340,200 mg rounded to 3.4 ×105 mg (must do this to have correct sig. figs!!)

How many centimeters are there in 1.5 yards? (1 yd = 3 ft, 1 ft = 12 in, 1 in = 2.54 cm) Answer: 137.16 cm rounded to 140 cm