When asked to estimate the number of steps required to walk the length of the Appalachian Trail,
Which student's answer is more sensible? Why?
Scientists pay careful attention to the way they write numerical values. They use only as many digits as they can justify, a practice we describe as providing only the significant digits. There is a connection between the number of significant digits in a written quantity and the uncertainty in that quantity.
2,000,000 8 x 10^(22) 0.03
2,100,000 8.9 x 10^(22) 0.030
Can you explain the mathematical basis for this connection?
What is the proper way to write each of the following quantities?
blue whale has mass M = 56.35 +/- 3.3 tonnes Joe "The Nose" Scarlatti erased N = 123 +/- 4 mobsters my measurements of pi yields pi = 3.1287356 +/- 0.0793234
Significant figures are like viruses: they infect any numbers they touch. If you combine two quantities, one with 5 significant figures and another with 1, then the result will have only 1 significant figure.
Try determining the result of the following calculations.
You can read more about significant figures in Section 1.5 of your textbook.
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