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We have two additional types of numbers we should talk about
exact numbers and approximate numbers. Exact numbers
arise from counting, while approximate numbers arise from
measurement or calculation. This is because we can never completely
measure something accurately. There is always some inaccuracy
involved.
This is important because our calculators will often provide us
an answer which has many decimal places in it and we need to know
just how many we should use.
Significant digits provide an indication of the accuracy of a
number. A digit which is 0 is significant only if it is not a place
holder.
Example
 | 18.651 has five significant digits since all digits are
non-zero |
| 10.80 has four significant digits since the measurement was
between 10.799 and 10.801 |
| 0.0276 has three significant digits since the two zeros are
place holders |
| 8500 has two significant digits since the measurement is
between 8450 and 8550 |
So in the example above, 8500, we assume that the measurement is
correct to the nearest 100th, since the 5 is the last
non-zero integer. |
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