Measurement, Part 2: Measurement & Uncertainty

There are two types of numbers in science: exact (counting) numbers and inexact (measurements and calculated quantities).  Exact or counting numbers represent objects.  For instance, a dozen eggs has exactly 12 eggs.  You can’t have 12.01 eggs.  Measurements and numbers based on calculations will always have some uncertainty. Significant digits are used to represent that uncertainty or the amount of confidence you have in a measurement.

Uncertainty occurs because we use equipment to make measurements.  You can only measure a length as exact as the increments on the ruler you are using.  Significant digits are the numbers we know with certainty plus one more that is estimated.

Basic Rules:

1. All non-zero digits are significant
2. All zeros between non-zero digits are significant
3. Zeros to the right of the decimal and to the right of a non-zero digit are significant
4. Zeros to the right of the decimal, but to the left of all non-zero digits are not significant
5. If there is no decimal, zeros to the right of the last non-zero digit are not significant

Rules for Calculations:

1. In addition and subtraction, use the LEAST number of DECIMALS.
2. In multiplication and division, use the LEAST number of SIGNIFICANT DIGITS.
3. Apply each rule using the order of operations.