APPENDIX 2

File: SIGFIG.DOC

The theory of significant digits is concerned with the useful and trustworthy digits in a number. Suppose you measure a person's height to the nearest centimeter as 63 cm. This means that you are sure of the 6 and have determined that the 3 is better than 2 or 4; therefore, both the 6 and the 3 are significant digits. A significant digit represents a number whose value is supported by a reliable measurement.

The number of significant digits recorded in a measurement depends partly on the measuring instrument and partly on what is being measured. If you are measuring length with a meter stick graduated in millimeters, then a fraction of the millimeter is the smallest reliable unit of measure you can use. If the object being measured does not have definite or sharp boundaries (for example, the length of your forearm), then your measurement may be less certain than the smallest reliable unit of your measuring instrument. If you can measure with certainty only to the centimeter, you are not justified in recording the measurement as 63.1 cm for that would imply that your measurement was reliable to the nearest tenth of a centimeter. You should instead record your measurement as 63 cm.

Any measurement you record during the semester must have an appropriate number of significant figures.

Let us review briefly the conventions we use concerning significant figures:

SigFig Rules

(For Conventional Numbers)

(1) All non-zero digits in a number should be significant. For example, 63.1 cm has three significant digits.

(2) Zeros that lie between two non-zero digits are significant. For example, the zero in 309 m is significant.

(3) Zeros following the last non-zero digit of a number are not significant but merely indicate order of magnitude. If, however, a bar is placed over the following zeros, then they are significant. For example, 567,000 has three significant digits whereas has six significant digits.

(This conversion is not often used. See the comments about scientific notations below for a better convention).

(4) If a number contains a decimal point

(a) Zeroes that lie between the decimal point and the first non-zero digit merely indicate order of magnitude. For example, 0.000567 has three significant digits.

(b) Zeros following non-zero digits are significant. For example, 5670.00 has six significant digits.

By using scientific notation, we can replace the above rules by a single rule.

Sigfig Rules

(For Scientific Numbers)

All digits in a number that is written in scientific notation are significant.

For example:

The rules for determining the number of significant digits in a final answer are given below.

(1). When adding or subtracting numbers, the result should not be carried beyond the first column having a doubtful figure.

For example,

8.16 + 74 = 82, not 82.16.

(2). When multiplying or dividing, the result should have the same number of digits as the least significant number used in the calculation. For example, 8.3 x 1045 = 8700, not 8672.5.

In all labs be sure that all the measured and calculated numbers that you record have the intended number of significant digits.