Chapter 3 Measurement Dimensional Analysis Objectives Construct conversion

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

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/cm 3) to kg/m 3.

Dimensional analysis problems Answer 2 • Given – Gold = 19. 3 g/cm 3 – Gold = ? kg/m 3 • 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 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 micrometers (µm) = 1 m • 1, 000, 000 nanometers (nm) = 1 m