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Accuracy Vs. Precision

Measuring and obtaining data experimentally always comes with some degree of error.

Human or method errors & limits of the instruments

We want BOTH accuracy AND precision

MEASUREMENTS AND CALCULATIONS IN CHEMISTRY

Selecting the right piece of equipment is key

Beaker, Graduated Cylinder, Buret?

Measuring 1.5 grams with a balance that only reads to the nearest whole gram would introduce a very large

error.

EXPERIMENTAL ERROR

So what is Accuracy?

Accuracy of a measurement is how close the measurement is to the TRUE value

“bull’s-eye”

ACCURACY

An experiment calls for 36.4 mL to be added

Trial 1: delivers 36.1 mLTrial 2: delivers 36.6 mL

Which is more accurate???Trial 2 is closer to the actual value

(bull’s-eye), therefore it is more accurate that the first delivery

ACCURACY

Now, what about Precision??

Precision is the exactness of a measurement.

It refers to how closely several measurements of the same quantity made in

the same way agree with one another.

“grouping”

PRECISION

Maximizing Accuracy and Precision will help to Minimize ERROR

Error is a measure of all possible “mistakes” or imperfections in our lab data

As we discussed, they can be caused from us (human error), faulty instruments (instrumental error), or from simply selecting the wrong piece of equipment (methodical error)

ERROR

Error can be calculated using an “Accepted Value” and comparing it to the

“Experimental Value”

• The Accepted Value is the correct value based on reliable resources (research, textbooks, peers, internet)

• The Experimental Value is the value YOU measure in lab. It is not always going to match the Accepted value… Why not??

ERROR

Error is measured as a percent, just as your grades on a test.

Percent Error = accepted – experimentalx100%

accepted

• This can be remembered as the “BLT” equation:

bigger minus littler over the true value

ERROR

Significant Figures (SigFigs) of a measurement or a calculation

consist of all the digits known with certainty as well as one estimated,

or uncertain, digit

ALWAYS ESTIMATE one more digit when reading

measurements!!

SIGNIFICANT FIGURES

Homework:

“Reading instruments” practice

1. Nonzero digits are always significant2. Zeros between nonzero digits are

significant3. Zeros in front of nonzero digits are

NOT significant4. Zeros both at the end of a number

and to the right of a decimal point ARE significant

5. Zeros at the end of a number but to the left of a decimal point may or may not be significant

RULES FOR DETERMINING SIGFIGS

5. Zeros at the end of a number but to the left of a decimal point may or may not be significant

If a zero has not been measured or estimated, it is NOT significant. A decimal point placed after zeros indicates that the zeros are significant.

i.e. 2000 m has one sigfig, 2000. m has four

SIGFIGS

How many sigfigs do the following values have?

46.3 lbs 40.7 in. 580 mi

87,009 km 0.009587 m 580. cm

0.0009 kg 85.00 L 580.0 cm

9.070000 cm 400. L580.000 cm

PRACTICE WITH SIGFIGS

Calculators DO NOT present values in the proper number of sigfigs!

Exact Values have unlimited sigfigsCounted values, conversion factors,

constants

CALC WARNING

Multiplying / DividingThe answer cannot have more sigfigs than the value with the smallest number of original sigfigs

ex: 12.548 x 1.28 = 16.06144

CALCULATING WITH SIGFIGS

This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!

Multiplying / DividingThe answer cannot have more sigfigs than the value with the smallest number of original sigfigs

ex: 12.548 x 1.28 = 16.06144

= 16.1

CALCULATING WITH SIGFIGS

This value only has 3 sigfis, therefore the final answer must ONLY have 3 sigfigs!

How many sigfigs with the following FINAL answers have? Do not calculate.

12.85 * 0.00125 4,005 * 4000

48.12 / 11.2 4000. / 4000.0

PRACTICE

Adding / SubtractingThe result can be NO MORE certain than the least certain number in the calculation (total number)

ex: 12.4 18.387

+ 254.0248 284.8118

CALCULATING WITH SIGFIGS

The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal.

Adding / SubtractingThe result can be NO MORE certain than the least certain number in the calculation (total number)

ex: 12.4 18.387

+ 254.0248 284.8118 =

284.8

CALCULATING WITH SIGFIGS

The least certain number is only certain to the “tenths” place. Therefore, the final answer can only go out one past the decimal.

Least certain number (total number)

Both addition / subtraction and multiplication / division

Round using the rules after each operation.

Ex: (12.8 + 10.148) * 2.2 =22.9 * 2.2 = 50.38 = 50.

CALCULATING WITH SIGFIGS

• Scientific Notation – a number written as the product of two values:

• A number out front &

• A x10 to a power

• This notation allows us to easily work with very, very large numbers or very, very small numbers.

SCIENTIFIC NOTATION

• The number out front MUST be written with ONLY one value prior to the decimal point

Examples: a. 3.24x104g b. 2.5x107mL= 32,400 grams = 25,000,000

mL

SCIENTIFIC NOTATION

• The exponent (x104) value can have a power that is positive or negative, depending on if you are dealing with a SMALL number or a LARGE number

Examples: a. 8.55x104g b. 4.67x10-4 L= 85,500 grams = 0.000467

Liters

SCIENTIFIC NOTATION

Addition / Subtraction

6.2 x 104 + 7.2 x 103

SCIENTIFIC NOTATION

Addition / Subtraction

6.2 x 104 + 7.2 x 103 First, make exponents the same

62 x 103 + 7.2 x 103

Do the math and put back in Scientific Notation

SCIENTIFIC NOTATION

Multiplication / Division

3.1 x 103 * 5.01 x 104 The “mantissas” are multiplied and the

exponents are added.(3.1 * 5.01) x 103+4

16 x 107 = 1.6 x 108

Do the math and put back in Scientific Notation (with correct number of

sigfigs)

SCIENTIFIC NOTATION

Homework:

SigFigs Worksheet