Significant Figures or Digits Take notes, this is important!

What are Significant Digits? The Important Numbers Representatives of the precision and accuracy of measurements. Absolutely Necessary!

Why Do We Have Significant Digits? They limit the number of decimal places They give our calculations relevance They make students crazy

Identifying Significant digits A SigFig is: All nonzero numbers Leading zero non significant Captive zeros (zeros in between nonzero numbers) Trailing zeros when a decimal is present

Identifying Significant Digits A SigFig is not: Leading zeros Trailing zeros when there is no decimal

Trailing - If a decimal is present Are Zeros Significant? Trailing - If a decimal is present Leading – Never Captive – Always

Identifying Significant Digits 12,345.67 All are SigFigs 1,234,000 4 SigFigs 0.000123 3 SigFigs 1,020,304 All are SigFigs 0.0120340 6 SigFigs 1.230 x 10-6 4 SigFigs 0.0001000 4 SigFigs

Using Significant Digits Adding and Subtracting - The final calculated answer should have the same # of decimal places as the measurement that is the least accurate (least # of decimal places). Multiplying and Dividing- The final calculated answer should have the same # of SigFigs as measurement with least # of Sig Figs.

Rounding Rules If a digit is to be cut off, and it is less than 5, the # before the cut remains the same. If a digit is to be cut off, and it is greater than or equal to 5, then the # before the cutoff is increased by 1. Always wait to round #’s until the last calculation is completed.