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