2.4 Game 2302-0340 scientific notation and significant figures

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
  • Accuracy and precision
  • Scientific notation
  • Significant figures
• Discussion and sample code
• Run the scripts
• Miscellaneous

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The purpose of this module is to explain the use of scientific notation and significant figures.

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1 . Examples of significant figures.
• Figure 2 . Screen output from Listing #1.
• Figure 3 . Screen output from Listing #2.
• Figure 4 . Behavior of the toPrecision method.
• Figure 5 . Screen output from Listing #3.

Listings

• Listing 1 . An exercise involving addition.
• Listing 2 . An exercise involving multiplication.
• Listing 3 . An exercise involving combined operations.

General background information

This section will contain a discussion of accuracy, precision, scientific notation, and significant figures.

Accuracy and precision

Let's begin with a brief discussion of accuracy and precision. These two terms are often used interchangeably in everyday conversation, but they have very differentmeanings in the world of science and engineering.

Accuracy

In science and engineering, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual (true) value.

Precision

The precision of a measurement system (also called reproducibility or repeatability) is the degree to which repeated measurements under unchangedconditions show the same result.

Four possibilities

A measurement system can be:

• Both accurate and precise.
• Accurate but not precise.
• Precise but not accurate.
• Neither accurate nor precise.

A hypothetical experiment

Consider an experiment where a firearm is clamped into a fixture, very carefully aimed at a bulls eye on a downrange target, and fired six times.(Although you may never have seen or touched a firearm, you probably have a pretty good idea of how they behave.)

If the six holes produced by the bullets in the target fall in a tight cluster in the bulls eye, the system can be considered to be both accurate andprecise.

If all of the holes fall in the general area of the bulls eye but the cluster is not very tight, the system can be considered to be accurate but not precise.

If all of the holes fall in a tight cluster but the cluster is some distance from the bulls eye, the system can be considered to be precise but not accurate.

If the holes are scattered across a wide area of the target, the system can be considered to be neither accurate nor precise.