the preceding fraction. The answer is in milligrams because this is the only unit
remaining and it assures you that the correct operations have been performed in
the conversion.
Another Example
Dimensional analysis is used in examples throughout this book.
Precision, Accuracy, and Uncertainty
Two other factors to consider in measurement are precision and accuracy.
Precision indicates the reliability or reproducibility of a measurement. Accuracy
indicates how close a measurement is to its known or accepted value.
TIP
Accuracy is how close you have come to the true value.For example, suppose you were taking a reading of the boiling point of pure
water at sea level. Using the same thermometer in three trials, you record 96.8,
96.9, and 97.0 degrees Celsius. Since these figures show a high reproducibility,
you can say that they are precise. However, the values are considerably off from
the accepted value of 100 degrees Celsius, so we say they are not accurate. In this
example we probably would suspect that the inaccuracy was the fault of the
thermometer.
Regardless of precision and accuracy, all measurements have a degree of
uncertainty. This is usually dependent on one or both of two factors—the
limitation of the measuring instrument and the skill of the person making the
measurement. Uncertainty can best be shown by example.
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Precision is how repeatable the results are.The graduated cylinder in the illustration contains a quantity of water to be
measured. It is obvious that the quantity is betwen 30 and 40 milliliters because
the meniscus lies between these two marked quantities. Now, checking to see
where the bottom of the meniscus lies with reference to the ten intervening