Exact and Approximate Numbers

Problems in agriculture use two different types of numbers, exact and approximate. The two common examples of exact numbers are those obtained by counting and ratios. For example, if you count the number of horses in a pen and arrive at 10, you have exactly 10 horses, not 10 and 1/2 or 9 and 3/4. Ratios are exact numbers because 3/4 of a circle is exactly 3/4 of a circle. One note of caution about ratios, ratios expressed as a decimal, say, 2/3 = 0.6666666..., are approximate numbers because some ratios expressed as a decimal contain repeating digits.

Any number obtained by a measurement is an approximate number. The actual value of an approximate number is uncertain because all measuring devices have a limit to their precision. If you have a ruler that is graduated in 1/16 of an inch, then the ruler is only precise to the nearest 1/16 of an inch. The following example illustrates this point.

In Figure 2.1, the length of the rectangle is not aligned with any of the marks on the scale (ruler). You must record the length of the box to the last shorter reading, 2-9/16's, or the next longer reading, 2-5/8. Regardless of the value you choose, the answer you record is only close to the actual length, and thus is an approximate number. If the desire is to reduce the amount of uncertainty in the measurement, then a ruler with higher precision, such as 1/32's of an inch should be used.

When approximate numbers are used, digits can be introduced into the problem, that are not accurate (significant). If these digits are included, the accuracy of the answer may decrease with every computation. The potential for error is especially great if a calculator is used because most calculators show eight or nine numbers, regardless of their significance to the problem. The task of the calculator operator is

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FIGURE 2.1. Example of an approximate number.

FIGURE 2.1. Example of an approximate number.

to determine how many digits are significant and to round accordingly. Determining significant figures is discussed in more detail in the following section.

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