Significant figures

• Significant Figures - The number of digits you can read from an instrument (including exactly one estimated digit).
  • On a digital instrument, the last digit you can see is always estimated
  • On an analog instrument, it is up to you to estimate the final digit by interpreting the position of the marker on the graduated scale.
• interesting fact: The meniscus in liquid measurements is a result of surface tension competing with adhesion of the liquid to the container.
  • If the liquid wants to stick to the container, the meniscus will look like a 'u'
  • If the liquid is repelled by the container, it will be humped upward like a droplet of water
• Accuracy vs. Precision
  • Accuracy indicates how close a measurement is to the true value
  • Precision indicates how close measurements are to each other (or how consistent the measurements are).
• Significant figures ensure that the precision of our computed answers matches the precision of our measurements
• They tell us how to combine different measurements with math, and come up with a reasonable answer.
• On the subject of hobbits (or zeroes)
  1. Leading zeroes are never significant
  2. Zeroes sandwiched between non-zero digits are always significant
  3. Zeroes at the end are significant, but only if the number has a decimal point
  4. Zeroes at the end are ambiguous if there is no decimal point
• Adding and subtracting numbers while respecting sigfigs
  • The answer has the same number of digits after the decimal point as the least-precise input
  • The least-precise input is the one with fewer digits after the decimal point.
• Multiplying and Dividing
  • The answer has the same number of sig figs as the least-precise input
  • The least-precise input is the one with fewer significant figures
• After you add, subtract, multiply, or divide, you use the extra digits beyond the sig figs to round the last sig fig.