Significant Figures Any digit in a measurement that is known with certainty plus one final digit, which is somewhat uncertain or estimated.

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Presentation transcript:

Significant Figures Any digit in a measurement that is known with certainty plus one final digit, which is somewhat uncertain or estimated.

Making Measurements with Sig Figs Record every digit you know for certain, plus one that you estimate On this graduated cylinder, we know the 10s place and the 1s place for certain (there are lines), so we will estimate the tenths place The volume is 52.7 mL

All nonzero digits are significant Rule # 1 All nonzero digits are significant Example: 2.14 has 3 sig figs

Zeroes between nonzero digits are significant. Rule # 2 Zeroes between nonzero digits are significant. Example: 2001 has 4 sig figs

Trailing zeroes are significant ONLY if there is a decimal point. Rule # 3 Trailing zeroes are significant ONLY if there is a decimal point. Example: 4000 has 1 sig fig 4000. has 4 sig figs 4000.0 has 5 sig figs

Rule # 4 Zeroes preceding the first nonzero digit in a number are NEVER significant. Example: 0.00004 has 1 sig fig

How many sig figs? 227 cm 0.0350 L 700 s 2.50 x 1054 atoms

Rounding Rules Round up if the trailing number is 5 and above. 4566.89 Rounded to 4 significant figures would be 4567 Leave preceding digit the same if the trailing number is 4 and below. 1234.456 Rounded to 4 significant figures would be 1234

Round these to 3 sig figs! 2.457 2.453 9.900 x 10-5 0.00034824 300001

Sig Fig Addition/Subtraction Rule Record your answer according to the number having the least number of decimal places (the least accurate) Example: 2 cm + 12.0 cm = 14 cm

Sig Fig Multiplication/Division Rule Record your answer according to the number having the least total number of significant figures Exceptions: do not include constants (ex. pi, the number of sides a square has, etc.) in your determination of the number of sig figs Example: 2.0 cm x 12.0 cm = 24 cm2

Accuracy The extent to which a measurement approaches the true value of a quantity Is this accurate?

Precision The extent to which a series of measurements of the same quantity made in the same way agree with each other Is this accurate, precise, neither, or both?