Accuracy vs. Precision

• Some people would say that Trial 2 would be more accurate than Trial 1

• But Accuracy is how close our measurement is to the actual value and experiments would not be run if we already know the actual value--- So

• The correct term is Precision

Calculations involving Precision

• All measurements contain an estimated digit

• Example: If the meniscus (the bottom of the concave surface) of water is between interval gradations of a graduated cylinder, we can estimate its value

• So we could measure 15.8mL for a volume when the liquid’s meniscus is between 15 and 16mL

• We know for sure that the liquid is greater than 15 mL and less than 16 mL

• The .8 mL portion of our measurement is only an estimate or the uncertainty of our measurement

• If we could use a more sensitive instrument we could refine our measurement.

• Nevertheless, it will always contain an estimated digit or figure at the end

• The last digit in all measurements are therefore only an estimate

• So if we used a graduated cylinder divided into tenths of a milliliter we could refine our measurement

• We could determine it to be between 15.7 and 15.8 mL; we know that it is greater than 15.7 mL for sure according to our graduated cylinder BUT we can also estimate what the value is between the two intervals giving us 15.75 mL

• Is our new reading more precise than the first? Yes, but it still has an estimated digit – the .05mL value!

• What is the danger, if any, in performing calculations with measurements that have an estimated digit?

• Let’s see: What is the cylinder’s surface area if we measure its diameter to be 6.58cm?

• A = πr2 = π(3.29)2

• Our calculator value is 34.00491304cm2

• BUT was our original measurement carried out to the same number of places past the decimal?

Significant Figures/Digits to the Rescue

• Rules for Counting SigFigs; Count– All digits from 1 to 9– Zeros in between nonzero digits– All zeros following nonzero digits (these zeros

are called “trailing zeros”)

• Do NOT Count zeros in front of a value (these are called “leading zeros”) because they only serve to set the decimal point

• Exact Numbers – those by definition or counting numbers are infinite as to sigfigs

• 156 g has 3 sigfigs• 0.2608 m has 4 sigfigs• 120.50 L has 5 sigfigs• 0.05003 s has 4 sigfigs• 7.2 oC has 2 sigfigs• 12 students is infinite

• How can be tell the reader the number of sigfigs if a measurement like 2000 g?

• Is it accurate to only the thousands or the hundreds or the tens of grams?

• We use Scientific Notation to solve our dilemma – M x 10n

• What ever digits are used in the M portion of our notation are significant

• 2.0 x 103 g has 2 sigfigs• 2 x 103 g has 1 sigfig• 2.00 x 103 has 3 sigfigs• Got it?

Back to Calculations with SigFigs• Multiplication/Division• The Quotient or Product has to contain

the same number of sigfigs as the starting measurement with the least number of sigfigs

• 2.34cm x 3.6cm = 8.424cm2 = 8.4cm2

There are only 2 sigfigs in “3.6”• 4.689cm/ 2.3 x 103 = 2038.695652cm =• 2.0 x 103 cm as we can only have 2 sigfig

• Formula given another way• = l observed value – accepted value l x

100 accepted value• An example: You determine the atomic

mass for aluminum to be 28.9 amu whereas the literature cited value is 27.00amu.

• What is your percent error?• Filling in your formula you get• l 28.9 – 27.00 l x 100 = 7.04%

(7.037037) 27.00

•That’s all Folks…