MEASUREMENT (A Quantitative Observation) MEASUREMENTS always have 2 things: Number & Unit All measurements have error in them! A measurement consists of all known digits that can be known accurately PLUS one digit that is ESTIMATED. The estimated digit is always at the END of the number in a measurement.

MEASUREMENT & Degrees of Error The closer a measurement is to the true value, the more accurate the measurement. Accurate measurements are “more correct” and closer to the true value. Accuracy = Correctness. How close a series of measurements are to one another is called precision. Precise measurements are close in value to one another; repeated measures are precise. Precision = Reproducibility.

Accuracy vs. Precision Another example: a 5 lb bag of potatoes is weighed by 3 people, 3 times each. Person lbs 4.8 lbs 4.85 lbs Person lbs 3.5 lbs 5 lbs Person lbs 4.1 lbs 4.2 lbs Good Accuracy Good Precision Poor Accuracy Poor Precision Poor Accuracy Good Precision

Determining Error Accepted value is the correct value based on reliable references. Reference: boiling point of water is 100.0°C Experimental value: temperature of boiling water measured to be 99.1°C ERROR = experimental – accepted value

ERROR = (99.1°C – °C) = –0.9 °C (-) means your measurement was less than the number of the true value. (+) means your measurement is greater than the true value. PERCENT ERROR is an absolute value: %ERROR = (0.9/100) x 100 = 0.9%

A way to express very large or very small numbers easily. Example: seconds = x seconds = x minutes minutes SCIENTIFIC NOTATION

Practice (1) g  5.65 x g (2) s  5.65 x 10 5 s (3) min  x 10 4 min (4).0010 L  1.0 x L

Measurement Limitations ALL measurements have error in them! A measurement consists of all known digits that can be known accurately PLUS one digit that is estimated. The estimated digit is always at the end of the number in a measurement. All of the digits that are known in a measurement are significant figures. Fewer significant figures = more rounding in a measurement = more error.

What are the following lengths (in meters)? (A) (B) (C)

ANSWERS (A) 0.3 m (1 decimal place) (B) 0.26 m (2 decimal places) (C) m (3 decimal places)

What is the density of a sample with a mass of g and a volume of 13.2 mL? A. 1.9 g/mL B g/mL C g/mL D g/mL APPLYING SIG FIGS to MEASUREMENT: HINT: Your FINAL answer cannot be more accurate than the least accurate measurement.

What is the density of a sample with a mass of g and a volume of 13.2 mL? A. 1.9 g/mL B g/mL C g/mL D g/mL APPLYING SIG FIGS to MEASUREMENT: Because 13.2 mL is accurate to only one decimal place, the answer can be no more accurate than one decimal place.

Easy Rules To Sig Figs ALL trailing zeros in a non-decimal are NOT significant (they act as placeholders only) ALL leading zeros in a decimal are NOT significant (they act as placeholders only) Sandwhiched zeros count (i.e. 101, 0.101) In a decimal, if the zero in question has a number 1 thru 9 before it anywhere in the number, it is significant! (i.e )

Putting It ALL Together

the speed of light = m / s 9 significant figures (sig figs) x 10 8 m/s 8 sig figs = x 10 8 m/s 7 sig figs = x 10 8 m/s 6 sig figs = x 10 8 m/s 5 sig figs = x 10 8 m/s 4 sig figs = x 10 8 m/s 3 sig figs = 3.00 x 10 8 m/s 2 sig figs = 3.0 x 10 8 m/s 1 sig figs = 3 x 10 8 m/s

ROUNDING = x 10 8 = x 10 8 = x 10 8 = x 10 8 = x 10 8 = 1.23 x 10 8 = 1.2 x 10 8 = 1 x 10 8

Determine the Significant Figures 1.0 blah blah 100 blah 100. blah 0.10 blah 0.01 blah blah 101 blah

Answers 1.0 blah 2 sig figs blah 10 sig figs 100 blah 1 sig fig 100. blah 3 sig figs 0.10 blah 2 sig figs 0.01 blah 1 sig fig blah 2 sig figs 101 blah 3 sig figs

Answers in Scientific Notation 1.0 x 10 0 blah 2 sig figs x 10 8 blah 10 sig figs 1 x 10 2 blah 1 sig fig 1.00 x 10 2 blah 3 sig figs 1.0 x blah 2 sig figs 1 x blah 1 sig fig 1.0 x blah 2 sig figs 1.01 x 10 2 blah 3 sig figs