Chapter 3: Measurement: Dimensional Analysis

Objectives Construct conversion factors from equivalent measurements Apply the techniques of dimensional analysis to a variety of conversion problems Solve problems by breaking the solution into steps Convert complex units, using dimensional analysis

Conversion factors Conversion factor used in dimensional analysis ratio of equivalent measurements. example: 24 hrs = 1 day They represent the same amount of time but are expressed with different numbers and units used in dimensional analysis usually written as a fraction or

Units arithmetic Multiplication of units Division of units add the exponents together 3 m x 2 m = 6 m2 8 cm3 x 2 cm2 x 1 cm = 16 cm6 Division of units exponents and/or entire units cancel Addition/subtraction of units Units don’t change, but must be same before add/subtract 8 mi - 5 mi = 3 mi 2

Dimensional analysis Dimensional analysis way to analyze and solve problems using the units, or dimensions, of the measurements. form of problem-solving figure out units it takes to get from start to finish line up all our conversion factors as fractions and cancel units that appear in both the numerators and denominators.

Dimensional analysis practice Question 1 How many seconds are in 3 weeks?

Dimensional analysis practice Answer 1 Given 3 weeks ? seconds What We Know 1 week = 7 days 1 day = 24 hr 1 hr = 60 min 1 min = 60 sec Work

Dimensional analysis practice Question 2 Convert gold’s density (19.3 g/cm3) to kg/m3.

Dimensional analysis problems Answer 2 Given Gold = 19.3 g/cm3 Gold = ? kg/m3 What We Know 1000 g = 1 kg 100 cm = 1 m Work

Conversion memorization (for now) US to Metric 1 in = 2.54 cm 454 g = 1 lb Metric larger 1 megameter (Mm) = 1,000,000 m 1 kilometer (km) = 1000 m Metric smaller 10 decimeters (dm) = 1 m 100 centimeters (cm) = 1 m 1,000 millimeters (mm) = 1 m 1,000,000 micrometers (µm) = 1 m 1,000,000,000 nanometers (nm) = 1 m