1.2: error and uncertainty
important number-related concepts in science
units of measurement
measurements vs. calculations
significant figures
dimensional analysis
accuracy and precision
accuracy: how close a measurement is to the real or accepted value of a quantity
correctness
precision: the proximity of several measurements to each other
reproducability
when we measure in science, we compare a physical quantity that we are interested in understanding to a known physical quantity
two issues must be confronted when measuring:
possibility of error
unavoidable uncertainty
error: the difference between a measurement and the actual or accepted value for the measurement
percent error = |[(measured value - accepted value)/accepted value] x 100|
uncertainty in measurement
different instruments of measurement have different degrees of precision and uncertainty
all measured numbers have some degree of inaccuracy
sources of measurement error
systematic error: unavoidable error
errors that consistently cause measurement values to be too large or too small
can be caused by faulty equipment
eg. mis-calibrated balances, inaccurate meter sticks
human error: avoidable error
can occur when equipment is used incorrectly
eg. reading from the wrong end of a meter stick, converting units incorrectly
random error: uncertainty—expected and unavoidable
when variations in the measurements occur without a predictable pattern
if repeated measurements are made, random error causes the measured value to vary, sometimes above or below the actual measured value
causes uncertainty in measurements
addressed by averaging measurements
can be minimized but not avoided entirely
measurements are inexact (uncertain)
measurements are inexact because scientific instruments have limitations
always a degree of uncertainty
some balances measure to ±0.01g and others to 0.0001g
exact numbers
counted
eg. there are exactly 13 donuts in the bakery box
are given as a definition (ie. conversion factors)
eg. there are 2.54cm in 1 inch
important number-related concepts in science
units of measurement
measurements vs. calculations
significant figures
dimensional analysis
accuracy and precision
accuracy: how close a measurement is to the real or accepted value of a quantity
correctness
precision: the proximity of several measurements to each other
reproducability
when we measure in science, we compare a physical quantity that we are interested in understanding to a known physical quantity
two issues must be confronted when measuring:
possibility of error
unavoidable uncertainty
error: the difference between a measurement and the actual or accepted value for the measurement
percent error = |[(measured value - accepted value)/accepted value] x 100|
uncertainty in measurement
different instruments of measurement have different degrees of precision and uncertainty
all measured numbers have some degree of inaccuracy
sources of measurement error
systematic error: unavoidable error
errors that consistently cause measurement values to be too large or too small
can be caused by faulty equipment
eg. mis-calibrated balances, inaccurate meter sticks
human error: avoidable error
can occur when equipment is used incorrectly
eg. reading from the wrong end of a meter stick, converting units incorrectly
random error: uncertainty—expected and unavoidable
when variations in the measurements occur without a predictable pattern
if repeated measurements are made, random error causes the measured value to vary, sometimes above or below the actual measured value
causes uncertainty in measurements
addressed by averaging measurements
can be minimized but not avoided entirely
measurements are inexact (uncertain)
measurements are inexact because scientific instruments have limitations
always a degree of uncertainty
some balances measure to ±0.01g and others to 0.0001g
exact numbers
counted
eg. there are exactly 13 donuts in the bakery box
are given as a definition (ie. conversion factors)
eg. there are 2.54cm in 1 inch
