# PHY 125 – Error, Uncertainty & Tolerance

Published on: Wed Jan 27 2010

Location ← Say “Position” instead
Si (System International) is also known as mks (meter, kilogram, second)
**Combination of Units**
You can combine the three base units to describe other things.
Speed = miles per hour [English System] or meters per Second [Si]
**Conversion of Units**
1 inch = 2.54cm
1 foot = 12 ● (inch) = 12 ● (2.54 cm)
**Significant Figures **
▬Relates to the # of significant figures given in the input
▬Rule of thumb

Area = Width ● Height = W ● H
If we say W = 1.00m, we mean 1.00m not 1.01m or .99m
If W = 1.00m and L = 3.33m, the Area = 3.33m²
What would happen in W = 1.01m and L = 3.33m?
Then we are stuck with this slightly odd number 3.3633m², but since the input numbers contain only three significant numbers, we need to round the slightly odd number to 3.36m².
What if W = 1.01m and L = 3.3m?
Then we need to round the slightly odd number (3.333) to 3.3m². Because we are rounding to the LEAST significant number of digits in the given input.
**Error and Uncertainty**
Error is not as common of a term, and this concept refers to the tolerance, i.e.: Margin for Error.
width = W = 1.000m ← accurate to millimeter = 1.000 ± .001m
1.000 ± .001m = width is in the range {1.001m , 0.999m} = W±∆W
±∆W = amount of variation in W
W = measurement
*****NOTE*****
To Determine the uncertainty of a measurement, repeat the measurement to find the distribution curve.
**Adding & Subtracting Uncertainty**
Perimeter = P = 2L + 2W
Perimeter with uncertainty
P±∆P
= 2(L±∆L) + 2(W±∆W)
= 2L+2W ±2∆W ±2∆L
Maximum Perimeter = P +2∆W + 2∆L
Minimum Perimeter = P -2∆W - 2∆L