Accuracy & Precision & Significant Digits

Accuracy & Precision What’s difference? Accuracy – The closeness of the average of a set of measurements to the true value. Ex. Density of Hg = 13.6 g/mL Trials – 13.6, 13.0, 14.2 g/mL

Accuracy & Precision Precision – The closeness of the values of a set of measurements to each other. Ex. Density of Hg = 13.6 g/mL Trials – 13.1, 13.0, 12.9 g/mL The true value does not matter in being precise.

Target Practice Accurate & Precise

Target Practice Accurate, not Precise

Target Practice Precise, not Accurate

Target Practice Not Accurate or Precise

Accuracy & Precision Experimental error – the lack of ability to measure anything to an exact value. Error is not a mistake, but a lack of certainty in the measurements. This leads to...

Significant Digits (or Significant Figures) Every digit in a measurement reflects the accuracy of that measurement. All the digits are known with certainty with the final digit being estimated.

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Triple Beam Balance

Volume Readings

Rules for Determining Significant Digits 1) Non-zero digits are always significant m cm 19 km

Rules for Determining Significant Digits 2) Any zeros between non-zero digits are always significant g mm 101 m

Rules for Determining Significant Digits 3) Any zeros to the left of all non-zero digits are NOT significant kg m g

Rules for Determining Significant Digits 4) Final zeros (zeros to the right of the last non-zero digit) with a decimal point are significant g 400 cm 400. cm m

Rules for Determining Significant Digits 5) In scientific notation, all of the coefficient digits are significant x 10 9 m x g

Rules for Determining Significant Digits 6) Numbers that are defined (exact measurements) do NOT limit the significant figures in a calculation m = 100 cm

Practice Sig Digits Determine the number of sig. digits in the following values.  750  750.   7005  755      7.5 x 10 3

Math with Sig Digs Addition and Subtraction The placement of the last significant digit in your answer is based on the measurement with the least amount of precision.

Math with Sig Digs Addition and Subtraction Ex) 3.95 g g g g 231.3g

Math with Sig Digs Ex) g − 4.513g 9.437g 9.44g

Math with Sig Digs Multiplication & Division The number of sig. digits in the measurement with the fewest sig. digits determines the number of sig. digits in your answer.

Math with Sig Digs Multiplication & Division Ex) 2.0 cm x cm 2.0 cm x cm = cm cm 2  24 cm 2

Math with Sig Digs Multiplication & Division Ex) 4.52 g / mL = g/mL = 1.28 g/mL

Practice with Math and Sig. Digits Correctly answer the following using proper significant digits.  3.89 m m  52 g – g  cm x cm x cm  42.0 g / mL

Scientific Notation 1.23 x  coefficient 10  base 9  exponent

Changing from Sci. Notation to Decimal Form Move the decimal to the left or right the same number of places as the exponent Positive – move to the right  Negative – move to the left  1.23 x x 10 -5

Changing from Decimal Form to Sci. Notation Count the number of time the decimal place is moved to get a number between 1.0 and 9.9. The number of moves is your exponent Original number > 10, positive exponent Original number < 1, negative exponent 4,200,