# Scientific Measurements Calculations, and Values.

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Scientific Measurements Calculations, and Values

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 mL Trial 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

1.Nonzero digits are always significant 2.Zeros between nonzero digits are significant 3.Zeros in front of nonzero digits are NOT significant 4.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 lbs40.7 in.580 mi 87,009 km0.009587 m580. cm 0.0009 kg85.00 L580.0 cm 9.070000 cm400. L580.000 cm PRACTICE WITH SIGFIGS

Calculators DO NOT present values in the proper number of sigfigs! Exact Values have unlimited sigfigs Counted values, conversion factors, constants CALC WARNING

Multiplying / Dividing The 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 / Dividing The 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 * 0.001254,005 * 4000 48.12 / 11.24000. / 4000.0 PRACTICE

Adding / Subtracting The 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 / Subtracting The 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. 3.24x10 4 gb. 2.5x10 7 mL = 32,400 grams= 25,000,000 mL SCIENTIFIC NOTATION

The exponent (x10 4 ) 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. 8.55x10 4 gb. 4.67x10 -4 L = 85,500 grams= 0.000467 Liters SCIENTIFIC NOTATION

Addition / Subtraction 6.2 x 10 4 + 7.2 x 10 3 SCIENTIFIC NOTATION

Addition / Subtraction 6.2 x 10 4 + 7.2 x 10 3 First, make exponents the same 62 x 10 3 + 7.2 x 10 3 Do the math and put back in Scientific Notation SCIENTIFIC NOTATION

Multiplication / Division 3.1 x 10 3 * 5.01 x 10 4 The “mantissas” are multiplied and the exponents are added. (3.1 * 5.01) x 10 3+4 16 x 10 7 = 1.6 x 10 8 Do the math and put back in Scientific Notation (with correct number of sigfigs) SCIENTIFIC NOTATION

Homework: SigFigs Worksheet