2 ACCURACY VS. PRECISIONIn labs, we are concerned by how “correct” our measurements areThey can be accurate and preciseAccurate: How close a measured value is to the actual measurementPrecise: How close a series of measurements are to each other
3 EXAMPLE The true value of a measurement is 23.255 mL Below are a 2 sets of data. Which one is precise and which is accurate?23.300, ,22.986, ,
4 SCIENTIFIC INSTRUMENTS In lab, we want our measurements to be as precise and accurate as possibleFor precision, we make sure we calibrate equipment and take careful measurementsFor accuracy, we need a way to determine how close our instrument can get to the actual value
5 SIGNFICANT FIGURESWe need significant figures to tell us how accurate our measurements areThe more accurate, the closer to the actual valueLook at this data. Which is more accurate? Why?25 cm25.2 cm25.22 cm
6 ANSWER25.22cmThe more numbers past the decimal, the closer you get to the true value.How do we determine how many sig. figs. we have?
7 SIGNIFICANT FIGURESSignificant figure – any digit in a measurement that is known with certainty plus one final digit, which is uncertainExample:4.12 cmThis number has 3 significant figuresThe 4 and 1 are known for certainThe 2 is an estimate
8 SIGNIFICANT FIGURESIn general: the more significant figures you have, the more accurate the measurementDetermining significant figures with instrumentationFind the mark for the known measurementsEstimate the last number between marks
9 SIGNIFICANT FIGURES Graduated cylinder Meter stick At your desk: Ruler Let’s look at some examples:Graduated cylinderMeter stickAt your desk:Ruler
10 RULES FOR SIGNIFICANT FIGURES Rule 1: Nonzero digits are always significantRule 2: Zeros between nonzero digits are significant40.7 (3 sig figs.)87009 (5 sig figs.)Rule 3: Zeros in front of nonzero digits are not significant(4 sig figs.)(1 sig figs.)
11 RULES FOR SIGNIFICANT FIGURES Rule 4: Zeros at the end of a number and to the right of the decimal point are significant85.00 (4 sig figs.)(10 sig figs.)Rule 5: Zeros at the end of a number are not significant if there is no decimal40,000,000 (1 sig fig)
12 RULES FOR SIGNIFICANT FIGURES Rule 6: When looking at numbers in scientific notation, only look at the number part (not the exponent part)3.33 x 10-5 (3 sig fig)4 x 108 (1 sig fig)Rule 7: When converting from one unit to the next keep the same number of sig. figs.3.5 km (2 sig figs.) = 3.5 x 103 m (2 sig figs.)
13 HOW MANY SIGNIFICANT FIGURES? 35.020.090020.003.02 X 1044000
15 ROUNDING TO THE CORRECT NUMBER OF SIG FIGS. Many times, you need to put a number into the correct number of sig figs.This means you will have to round the numberEXAMPLE:You start with 998,567,000Give this number in 3 sig figs.
16 ANSWER Step 1: Get the first 3 numbers (3 sig figs.) 998Step 2: Check to see if you have to round up or keep the number the sameYou need to look at the 4th number9985If the next number is 5 or higher, round upIf the next number is 4 or less, stays the sameTherefore = 999
17 ANSWERStep 3: Look at your 3 numbers and put them in scientific notation9.99Step 4: Count the number of places you have to move the decimal to get the exponent9.99 x 108
18 TRY THESE10,000 (3 sig. figs.)(2 sig. figs.)347,504,221 (3 sig. figs.)(2 sig. figs.)89,165,987 (3 sig. figs.)