Significant Figures or Digits
Imagine that a nurse takes a child's temperature. However, the mercury thermometer being used is marked off in intervals of one degree. There is a 98° F mark and a 99° F mark, but nothing in between. The nurse announces that the child's temperature is 99° F. How does someone interpret this information? The answer becomes clear when one has an understanding of significant digits.
The Importance of Precision
One possibility, of course, is that the mercury did lie exactly on the 99°F mark. What are the other possibilities? If the mercury were slightly above or below the 99°F mark (so that his actual temperature was, say, 99.1°F or 98.8°F), the nurse would probably still have recorded it as 99°F. However, if his actual temperature was 98.1°F, the nurse should have recorded it as 98°F. In fact, the temperature would have been recorded as 99° F only if the mercury lay within half a degree of 99°F—in other words, if the actual temperature was between 98.5°F and 99.5°F. (This interval includes its left endpoint, 98.5°F, but not its right endpoint, because 99.5°F would be rounded up to 100°F. However, any number just below 99.5° F, such as 99.49999°F, would be rounded down to 99°F.) One can conclude from this analysis that, in the measurement of 99°F, only the first 9 is guaranteed to be accurate—the temperature is definitely 90-something degrees.
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