Dimensional Analysis

Scientific problems and calculations often involve unit conversions, or changes from one unit to another. Dimensional analysis is a method of unit conversion.

Suppose you were counting a pile of pennies. If there were 197 pennies in the pile, how many dollars would the pennies be worth? To determine the answer, you need to know the conversion factor between pennies and dollars. A conversion factor simply shows how two units are related. In this case, the conversion factor is 100 pennies = 1 dollar. Determining that 197 pennies is equal to $1.97 is an example of a unit conversion.

In dimensional analysis, the conversion factor is usually expressed as a fraction. Remember that the two values in any conversion factor are equal to one another. So, the two values form a fraction with the value of 1. Look at the example below to see how dimensional analysis can be applied to an everyday problem.

Example

A student walked 1.5 kilometers as part of a school fitness program. How many meters did the student walk?

  1. 1.5 km = ? m

  2. 1 km = 1000 m

  3. 1000 m/1 km

  4. 1.5 km × 1000 m/1 km = 1500 m (cross out “km” in two places); 1.5 km = 1500 m

Applying Dimensional Analysis

There are many applications of dimensional analysis in science. The example below demonstrates the use of dimensional analysis to convert units.

Example

The average teenage girl needs about 2200 kilocalories of energy from food each day. How many calories is this equivalent to?

Use the following steps to convert kilocalories to calories.

  1. Determine the conversion factor that relates the two units.

    1 kilocalorie = 1000 calories

  2. Write the conversion factor in the form of a fraction.

    1000 calories/1 kilocalorie

  3. Multiply the measurement by the conversion factor.

    2200 kilocalories × 1000 calories/1 kilocalorie = 2,200,000 calories

End ofPage A-23

Table of Contents

Miller & Levine Biology
About the Authors
Changing the World of Biology Education
Contents
Diversity of Life: A Visual Guide DOL•1–DOL•64
Labs and Activities
Features
UNIT 1 The Nature of Life
1 The Science of Biology
2 The Chemistry of Life
Unit Project
UNIT 2 Ecology
3 The Biosphere
4 Ecosystems and Communities
5 Populations
6 Humans in the Biosphere
Unit Project
UNIT 3 Cells
7 Cell Structure and Function
8 Photosynthesis
9 Cellular Respiration and Fermentation
10 Cell Growth and Division
Unit Project
UNIT 4 Genetics
11 Introduction to Genetics
12 DNA
13 RNA and Protein Synthesis
14 Human Heredity
15 Genetic Engineering
Unit Project
UNIT 5 Evolution
16 Darwin's Theory of Evolution
17 Evolution of Populations
18 Classification
19 History of Life
Unit Project
UNIT 6 From Microorganisms to Plants
20 Viruses and Prokaryotes
21 Protists and Fungi
22 Introduction to Plants
23 Plant Structure and Function
24 Plant Reproduction and Response
Unit Project
UNIT 7 Animals
25 Introduction to Animals
26 Animal Evolution and Diversity
27 Animal Systems I
28 Animal Systems II
29 Animal Behavior
Unit Project
UNIT 8 The Human Body
30 Digestive and Excretory Systems
31 Nervous System
32 Skeletal, Muscular, and Integumentary Systems
33 Circulatory and Respiratory Systems
34 Endocrine and Reproductive Systems
35 Immune System and Disease
Unit Project
A Visual Guide to The Diversity of Life
HOW TO USE THIS GUIDE
THE TREE OF LIFE
Bacteria
Protists
Fungi
Plants
Animals
Appendices
Appendix A Science Skills
Appendix B Lab Skills
Appendix C Technology & Design
Appendix D Math Skills
Appendix E Periodic Table
Glossary
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q, R
S
T
U
V
W
X, Y, Z
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Credits
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