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Tutorial on the Use of Significant Figures
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All measurements are approximations--no measuring device can give perfect measurements without experimental uncertainty. By convention, a mass measured to 13.2 g is said to have an absolute uncertainty of 0.1 g and is said to have been measured to the nearest 0.1 g. In other words, we are somewhat uncertain about that last digit —it could be a "2"; then again, it could be a "1" or a "3". A mass of 13.20 g indicates an absolute uncertainty of 0.01 g.
The objectives of this tutorial are:
—Explain the concept of signficant figures.
—Define rules for deciding the number of significant figures
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(5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant figures.
The potential ambiguity in the last rule can be avoided by the use of standard exponential, or "scientific," notation. For example, depending on whether the number of significant figures is 3, 4, or 5, we would write 50,600 calories as:
5.06 × 104 calories (3 significant figures)
5.060 × 104 calories (4 significant figures), or
5.0600 × 104 calories (5 significant figures).

What is a "exact number"?

Some numbers are exact because they are known with complete certainty.
Most exact numbers are integers: exactly 12 inches are in a foot, there might be exactly 23 students in a class. Exact numbers are often found as conversion factors or as counts of objects.
Exact numbers can be considered to have an infinite number of significant figures. Thus, the number of apparent significant figures in any exact number can be ignored as a limiting factor in determining the number of significant figures in the result of a calculation.

Rules for mathematical operations

In carrying out calculations, the general rule is that the accuracy of a calculated result is limited by the least accurate measurement involved in the calculation.
(1) In addition and subtraction, the

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