Summing It All Up

• Every measurement has some uncertainty in it; reported values should not contain unknown information
• When making a measurement with a device having a marked scale (like a ruler, a dial, or a non-digital watch), always estimate the value one degree of accuracy beyond the scale of your measurement device.
• The last digit you report should be the first digit with uncertainty in it.
• These digits we are reasonably certain about (including the one with some uncertainty) are the significant figures, also called significant digits.
• Significant digits are identified by following a few conventions:
• Any non-zero digit in a reported number is significant.
• If a zero is found between significant digits, it is significant.
• Zeros to the right of the decimal place that are NOT merely place holders are significant; these significant zeros will be to the right of non-zero significant digits.
• Conventions about zeros at the end of a number and to the left of the decimal place vary. In these modules, such zeros will always be considered insignificant. You should, however, look in your textbook to determine that author's convention.
• When a whole number is known exactly, it can be treated as having an infinite number of significant figures even when the zeros are not written out.
• The uncertainty in a calculated value is determined by the uncertainty of the least certain original number.
• When multiplying or dividing two or more numbers, count the significant figures in each of the original numbers. Take the smallest of the numbers of significant figures. The product or quotient will have that minimum number of significant figures.
• When adding or subtracting two or more numbers, the last significant digit is the digit in the rightmost decimal place common to all the original numbers.
• When using numbers in calculations, it's a good idea to keep one digit beyond the significant digits. Once the final answer is calculated, it may be expressed with the correct number of significant digits.
• Several of these conventions are summarized in a helpful flow chart.