Errro Analysis Error

Why Bother? The knowledge we have of the physical world is obtained by doing experiments and making measurements. It is important to understand how to express such data and how to analyze and draw meaningful conclusions from it.

Why Bother? ALL measurements of physical quantities are subject to uncertainties. It is never possible to measure anything exactly. in order to draw valid conclusions the error must be indicated and dealt with properly.

Example: Your Height is 5' 8“. How accurate is this? The height of a person depends on : how straight she stands, Did she just got up from lying horizontally Did she has her shoes on How long her hair is How her hair is made up. A quantity such as height is not exactly defined without specifying many other circumstances.

That’s Not All….. Even if you could precisely specify the "circumstances," your result would still have an error associated with it. The scale you are using is of limited accuracy when you read the scale, you may have to estimate a fraction between the marks on the scale, etc.

The two essential components of a physical measurement (1) A numerical value (in a specified system of units) giving the best estimate possible of the quantity measured (2) the degree of uncertainty associated with this estimated value. For example, a measurement of the width of a table would yield a result such as 95.3cm +/- 0.1 cm.

Significant Figures Definition: The significant figures of a quantity are the meaningful digits in it. 1. Any digit that is not zero is significant

Significant Figures 2. Zeros between non zero digits are significant

Significant Figures 3. Zeros to the left of the first non zero digit are not significant = 3.4x = 1x = 4.16x10 -3

Significant Figures For numbers with decimal points, zeros to the right of a non zero digit are significant has three significant figures has two significant figures. For this reason it is important to keep the trailing zeros to indicate the actual number of significant figures.

Percent Error To express the magnitude of the error (or deviation) between two measurements scientists invariably use percent error.

Order of Magnitude Used to make a rough comparison between compare numbers. Order of Magnitude of 1 = 10 1 Order of Magnitude of 2 = 10 2 Order of Magnitude of 3 = 10 3 etc.

How to Find the Order of Magnitude of a number Write the number in Scientific Notation If the mantissa (left side) is greater than 5, then go up one more power. Example: 8.9 x 10 4 It is greater than 5.0x10 4 Therefore 8.9x 10 4 would have an Order of Magnitude of 5. **check: 89,000 is closer to 100,000 than 10,000.

Order of Magnitude NumberScientific Notation Greater than 5 In the mantissa Order of Magnitude x10 3 No x 10 3 Yes x x x 10 -3