Chapter 2 Section 2 Units of Measurement
Dimensional AnalysisPart 1
Chapter 2 Section 2 Units of Measurement
Everyone complains how they should be paid for the work they do at school! So, lets figure out how much money you would make in a school year!
Facts you need to know:
How long is your day?
How many days do you βworkβ a day?
How much do you get βpaidβ?
7 hours
180 days
$7.25/hour
Chapter 2 Section 2 Units of Measurement
What is your answer? $9135
How did you get your answer? Multiply all three answers?
Here is what it should look like:
180πππ¦π π₯7hππ’ππ 1πππ¦
π₯$7.251hππ’π
=$ 9135
Dimensional Analysis USES Conversion Factors
β’ A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other.
β’ example: How quarters and dollars are related
4 quarters 1 dollar1 1
1 dollar 4 quarters
0.25 dollar 1 quarter1 1
1 quarters 0.25 dollar
Section 2 Units of MeasurementChapter 2
Click below to watch the Visual Concept.
Visual Concept
Section 2 Units of Measurement
Conversion Factor
Chapter 2
Conversion Factors, continued
β’ Dimensional analysis is a mathematical technique that allows you to use units to solve problems involving measurements.
4 quarter? quarters 12 dollars 48 quarters
1 dollar
Section 2 Units of Measurement
β’ quantity sought = quantity given Γ conversion factor
β’ example: the number of quarters in 12 dollars
number of quarters = 12 dollars Γ conversion factor
Chapter 2
β’ example: conversion factors for meters and decimeters
Conversion Factors, continuedDeriving Conversion Factors
β’ You can derive conversion factors if you know the relationship between the unit you have and the unit you want.
1 m 0.1 m 10 dm
10 dm dm m
Section 2 Units of MeasurementChapter 2
Remember SI Conversions?
Section 2 Units of MeasurementChapter 2
Conversion FactorsSample Problem B SolutionExpress a mass of 5.712 grams in milligrams and in kilograms.
Given: 5.712 g
Unknown: mass in mg and kg
Solution: mg
1 g = 1000 mg
Possible conversion factors:
1000 mg 1 gand
g 1000 mg
1000 mg5 5. 7712 g m
g12 g
Section 2 Units of MeasurementChapter 2
Sample Problem B Solution, continuedExpress a mass of 5.712 grams in milligrams and in kilograms.
Given: 5.712 g
Unknown: mass in mg and kg
Solution: kg
1 000 g = 1 kg
Possible conversion factors:
Conversion Factors, continued
1000 g 1 kgand
kg 1000 g
1 kg5.712 g
10000.005
g712 kg
Section 2 Units of MeasurementChapter 2
Chapter 2 Section 2 Units of Measurement
A βNon Metric Basedβ example
Some βinsaneβ workout fanatics want to run marathons. They have marathons listed at 26.2 mi and 35 k races. Which is shorter?
Facts Needed:1 km = 0.625 mi
35ππ π₯0.625ππ1ππ
=21.9ππ
26.2πππ₯1ππ0.625ππ
=41.9ππ So which would you want to run?
Cool Conversion Tutorial Video
Watch this guy break down the steps for a conversionβ¦β¦
Chapter 2 Section 2 Units of Measurement
Link to Video