Uncertainty in Measurement

What is the Difference Between Accuracy and Precision? Accuracy: how close a measurement comes to the true accepted value Precision: degree of exactness or refinement of a measurement; also, how close a series of measurements are to one another. Because measurements differ in precision, when calculations are performed, significant digits MUST be taken into consideration

How Reliable Are Measurements? No measurement obtained in the lab is exact; ALL measurements have some error Sources: Instrumental error: instrument not calibrated correctly Human error: occur by chance or through bias Method error: incorrect procedure or poor design of experiment

What is Uncertainty? The degree of estimation used in a measurement Measurements are uncertain for two reasons: Instruments are never completely flawless Measuring always involves some estimation

What is Uncertainty? When measuring, write down all the certain digits that the instrument can give you plus one uncertain digit that you can estimate On a digital display, the last digit is the estimated digit On a scale, or graduations on equipment, the last digit must be estimated by the measurer

How Can the Uncertain Digit Be Determined? To determine the uncertain digit: Find the smallest increment on the scale of the instrument  increment: distance between markings on equipment Determine the value of each increment Estimate the value of the measurement between the two increments The uncertain digit is the one you guessed

Reading Values 37 mL, +/- 1 mL The 7 is uncertain

Reading Values 52.9 mL, +/- 0.1 mL The 9 is uncertain

Reading Values 76.0 mL, +/- 0.1 mL The 0 is uncertain

Reading Values 5.15 mL, +/ mL The last 5 is uncertain

What are Significant Figures?  Sig Figs indicate the uncertainty of your measurement Every measurement indicates these three things:  The value of the measurement  The units of the measurement  The precision of the measurement

Rules for Significant Figures Rules for determining the number of sig figs can be found on your handout.

Why Are Numbers Rounded? Numbers are rounded to that a final answer in a calculation of measurements will reflect the correct number of sig figs. The number of sig figs in the problem will determine the number of sig figs in the answer

How Are Numbers Rounded? Rounding rules can be found on your handout.

What are Standard Units? Numbers by themselves are not exact enough to describe properties of matter SI system: standard scientific system of measurement (also called metric system) Combinations of base units can be used to describe nearly all physical measurements

What are the Base Units? Length: meter (m) Mass: kilogram (kg) Time: second (s) Electric current: ampere (A) Temperature: Kelvin (K) Amount of substance: mole (mol) Luminous intensity: candela (cd)

How Can Scale Be Expressed Using Base Units? Prefixes used with base units establish appropriate scale Prefixes can modify the SI unit to match the scale

What are the Most Commonly Used Prefixes? Milli (m), Centi (c), Deci- 0.1 (d), Base Deca- 10(D), 10 1 Hecto-100 (H), 10 2 Kilo (k), 10 3

What are Derived Units? Derived units: created by multiplying or dividing the seven base units in various ways Examples: m/s, cm 3, g/mL

Is volume a derived unit? Yes! Volume = l x w x h By definition, 1 cm 3 = 1 mL