Measurements and their Uncertainty Chapter 3.1 Measurements and their Uncertainty

Using and expressing measurements Measurement = a quantity that has both a number and a unity **Measurements are fundamental to the experimental science! Therefore, it is important to be able to make measurements and to decide whether a measurement is correct.**

Using and expressing measurements International System of Measurement = SI These are the units typically used in Science Meter, kilogram, second, Kelvin, etc.

Scientific Notation Where a given number is written as the product of 2 #’s: a coefficient and 10 raised to a power Why?? Writing large numbers is prevalent in Science and very cumbersome. Ex) 1 g Hydrogen = 602,000,000,000,000,000,000,000 H atoms -or- 6.02 x 10 23 Coefficient = 6.02 Exponent = 23

Scientific Notation Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction.

Scientific Notation

Accuracy & Precision Accuracy = a measure of how close a measurement comes to the actual or true value. Precision = a measure of how close a series of measurements are to one another.

Accuracy & Precision To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of 2 or more repeated measurements.

Accuracy & Precision

Accuracy & Precision

Error Accepted (true) Value = the correct value based on reliable references Experimental value = the value measured in the individual situation Error = the distance between the accepted value and the experimental value.

Error Percent error = the ratio of an error to an accepted value.

Significant figures A number that includes all of the known digits plus one estimated digit. Measurements must always be reported to the correct # of significant figures because calculated answers often depend on the # of significant figures in the value used in calculation. See page 67 in text for meter sticks with different callibrations!!

Significant Figures Rules for recognizing significant figures Non-zero numbers are always significant. 72.3 g has three Zeros between non-zero numbers are always significant. 60.5 g has three All final zeros to the right of the decimal place are significant. 6.20 g has three

Significant Figures Rules for recognizing significant figures Zeros that act as placeholders are not significant. Convert quantities to scientific notation to remove the placeholder zeros. 0.0253 g and 4320 g each have three Counting numbers and defined constants have an infinite number of significant figures. 6 molecules 60 s = 1 min

Significant Figures in Calculations A calculated answer cannot be more precise than the least precise measurement from which it was calculated!

Significant Figures in Calculations Addition & Subtraction Round the answer to the same # of decimal places as the measurement with the least # of decimal places. The answer is 77.2

Significant Figures in Calculations Multiplication & Division Round the answers to the same # of sig. figs as the measurement with the least # of sig figs.

Multiplication & Division With Sig. figs Calculate the volume of a rectangular object with the following dimensions: length = 3.65 cm width = 3.20 cm height = 2.05 cm The answer is 23.9 cm3.