Precision and Significant Digits

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Imagine you have to take a measurement using the ruler shown below:

Figure 1.

Inches are marked in red. Centimeters are marked in blue. Millimeters are marked in green.

Here, our smallest unit of measurement is the millimeter. 1 Millimeter is our "Precision Unit"

When used correctly, the greatest possible error for this instument is half of its precision unit, or 1/2 of a Millimeter.

Figure 2.

Here, we've taken a measurement of 14.6cm. This measurement has three significant digits.

How do we count significant digits?

Counting Significant Digits
1. All nonzero digits are significant. 2. Zeros between significant digits are also significant. 3. Zeros used to show place values are not significant. 4. In numbers with a decimal point, all zeros to the right of a nonzero digit are significant.

Counting Significant Digits

1. All nonzero digits are significant.

2. Zeros between significant digits are also significant.

3. Zeros used to show place values are not significant.

4. In numbers with a decimal point, all zeros to the right of a nonzero digit are significant.

Below, we count the number of significant digits in four numbers:

Figure 3.