numbers and chemistry

• 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

measurement

• 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