Numbers - Foundations of Engineering - Lecture Slides, Slides of Civil Engineering

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Numbers

Numbers

• Accuracy and Precision
• Systematic Errors and Random Errors
• Uncertainty and Errors
• Significant Figures

Simple Error Analysis

• Real Numbers
  • are used to represent values of continuous variables or quantities
  • length of rod, mass of rock, velocity of a vehicle, etc.
• Integer Numbers
  • are used to represent values of discrete variables or quantities
  • number marbles, number of people, number of stars, etc.

• Accuracy
  • describes the nearness of a value to the correct or true value
  • A highly accurate measuring device will on average obtain values close to the true value.

Example: Precision vs. Accuracy

• An easy way to remember the difference between precision and accuracy is to consider patterns shot on a target.
• Consider the table shown on the next slide...

Yes No

Yes

No

Accurate

Precise

Target

Practice

Thought Problem

• If we measure the weight of a calculator and get values of 3.001 N, 3.000 N, 2.999 N, 3.000 N
• These numbers are precise enough for us to believe that if we measure in again we would get 3.000 ± .001 N.
• What if the actual weight is 2.5 N?
  • our scale is precise, but not accurate!

Italics means that students do not need to write it down.

Errors

 Random Errors

 errors that occur in a random nature  The presence of random errors is evident by the scatter in measured data.

 Repeating measurements and averaging the results will reduce the random error in the average.

 Engineers must be aware of the presence of systematic errors and eliminate those possible and try to quantify and correct for those remaining.

 Repeating measurements will not eliminate or reduce systematic errors.

Handout Team Exercise for Chapter 7 Allow the teams 6 minutes to complete #1. Professor asks one member from 6 random teams to explain their answer.

1. Identify the errors in the measurements below as systematic or random errors. The produce scale at the grocery store has water on it. The water runs off the produce. The timekeeper sneezes at he moment the runners cross the finish line. Measuring with a 100 feet tape that is actually 99.01 feet. Press the wrong key(s) on a calculator during a long calculation. Your airplane always seems to turn a bit to the right even when the controls are level. Early images from the Hubble Space Telescope were always blurry.

Clicker - Timekeeper

The timekeeper sneezes at he

moment the runners cross the finish

line.

A. Systematic Error

B. Random Error

Clicker - Facilitator

Measuring with a 100 feet tape that is

actually 99.01 feet.

A. Systematic Error

B. Random Error

Clicker – Any Team Member

Your airplane always seems to turn a

bit to the right even when the

controls are level.

A. Systematic Error

B. Random Error

Clicker - Any Team Member

Early images from the Hubble Space

Telescope were always blurry.

A. Systematic Error

B. Random Error