3C Dealing with Uncertainty

Review: Round to the nearest thousandth, tenth, ten, hundred:

6000
0.45232768
-12.001

Significant digits:

digits	significant	not significant
nonzero	x
zeros that follow a nonzero digit and right of decimal point: 4.20	x
zeros between nonzero digits or significant zeros: 4002, 30.0	x
zeros to the left of nonzero digits: 0.0006		x
zeros to the right of last nonzero digit, but before decimal point: 40,000		x, unless stated otherwise

Find the number of significant digits:

Random Errors: caused by random, inherently unpredictable events in the measurement process
Systematic Errors: caused by a problem in the measurement system that affects all measurements in the same way

Describe possible sources of random errors when computing the average income of 25 people, found by checking their tax returns.
We like to find out how many people have Aids by studying the medical records of Aids patients. Describe possible random and systematic errors.
The 2000 census reports that there are exactly 281,421,906 people living in the US. random and systematic errors?

Size of Error:
absolute error: measured value - true value
relative error: absolute error / true value

Find the absolute and relative error:

price of a gift purchase by mail order is listed as $18.50, but you are billed $19.00.
diameter of a ball bearing is supposed to be 0.1cm, but instead is 0.2cm.

Describing results:
accuracy: how close is the measurement to the real value
precision: amount of detail in the measurement (quality of the measuring instrument)

Which is more precise / accurate?

true height is 62.5 inches, a tape measure, which can be read to within 1/8 inch, gives a reading of 62 and 3/8 inch, a laser device gives a reading to nearest 0.05 inch shows 62.90 inches.

discuss possible sources of error and whether the statement is believable:

average temperature in January in LAgos, Nigeria is 88 degree.
the number of deaths due to AIDS in US as of 1997 is 390,242.

Combining measured numbers
+, -: sum/difference is rounded to the same precision as the least precise number in the problem
*, /: product/quotient is rounded the same number of significant digits as the number with the fewest significant digits

140 l - 1.09 l =
480 people are taxed for a total amount of $112.4 million. Average tax?

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