Chapter 2 Section 2 Units of Measurement Dimensional Analysis Part 1.
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Transcript of Chapter 2 Section 2 Units of Measurement Dimensional Analysis Part 1.
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 “work” a day?
How much do you get “paid”?
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:
180𝑑𝑎𝑦𝑠𝑥7h𝑜𝑢𝑟𝑠1𝑑𝑎𝑦
𝑥$7.251h𝑜𝑢𝑟
=$ 9135
Dimensional Analysis USES Conversion Factors
• 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.
• 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
• 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
• quantity sought = quantity given × conversion factor
• example: the number of quarters in 12 dollars
number of quarters = 12 dollars × conversion factor
Chapter 2
• example: conversion factors for meters and decimeters
Conversion Factors, continuedDeriving Conversion Factors
• 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 “Non Metric Based” example
Some “insane” 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
35𝑘𝑚 𝑥0.625𝑚𝑖1𝑘𝑚
=21.9𝑚𝑖
26.2𝑚𝑖𝑥1𝑘𝑚0.625𝑚𝑖
=41.9𝑘𝑚 So which would you want to run?
Cool Conversion Tutorial Video
Watch this guy break down the steps for a conversion……
Chapter 2 Section 2 Units of Measurement
Link to Video