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Unit 2.4: Dimensional Analysis - Understanding Numbers and Conversion Factors, Lecture notes of Dimensional Analysis

This unit covers the importance of using units with measured numbers in science, calculating ratios and conversions using units, and utilizing conversion factors for problem-solving. Students will learn how to perform calculations using the factor label method to ensure accurate results.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Unit 2.4 Dimensional Analysis
Teacher: Dr. Van Der Sluys
Objectives
Numbers with units
Ratios and Units
Conversion factors
Factor Label
Numbers With Units
All measured numbers in science
should be accompanied by units.
Without knowing the units it is
impossible to communicate appropriate
information to other scientists and draw
appropriate conclusions.
We will restrict our discussions to
metric units exclusively.
pf3

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Unit 2.4 Dimensional Analysis

Teacher: Dr. Van Der Sluys

Objectives

  • Numbers with units
  • Ratios and Units
  • Conversion factors
  • Factor Label

Numbers With Units

  • All measured numbers in science should be accompanied by units.
  • Without knowing the units it is impossible to communicate appropriate information to other scientists and draw appropriate conclusions.
  • We will restrict our discussions to metric units exclusively.

Ratios and Units

  • There are twelve eggs per dozen.
  • If you have 48 eggs, how many dozen eggs do you have? Solve the ratio for X. 12 eggs/dozen 48 eggs 12 eggs X dozen = 1 dozen 12 eggs 12 eggs = 1 dozen 1 dozen

Conversion Factors

  • A conversion factor is a number that has a combination unit, or “unit per unit”. Example: 12 eggs per dozen.
  • One can also use the inverse of this unit in a calculation. How many dozen per egg? 1/12 dozen/egg 1 dozen 12 eggs

Conversion Factors

  • Multiplying by a conversion factor is the same as multiplying by 1.
  • How many eggs are represented by 3.5 dozen? Multiply the information given in the question by the conversion factor so that the unit dozen appears in both the numerator and denominator, and therefore cancels. 12 eggs 1 dozen = 1 3.5 dozen x 12 eggs = 1 dozen given conversion factor