Rules for Significant Figures and Propagation of Uncertainty

Individual Numbers

1. Write the number in scientific notation.

2. Significant Zero’s

a. Zero’s that lie between two non-zero numbers

b. Zero’s that are at the end of a number on the right hand side of the decimal point.

Numbers that Result from Arithmetic Operations

+, -

1. Write all numbers so that the exponent is the same for each.

2. All digits to the left of the decimal point are significant.

3. Digits to the right of the decimal point:

a. Determine which value in the arithmetic problem contains the fewest places to the right of the decimal point.

b. Round the answer to the problem so that it contains the same number of digits to the right of the decimal point as the value determined in the previous step.

x, ¸

1. Determine which value contained in the arithmetic problem has the fewest significant digits.

2. Round the answer to the problem so that it contains the same number of digits (including those before and after the decimal point) as the value determined in step 1.

Logarithms

1. All digits, in the answer, to the left of the decimal point (characteristic) are significant.

2. The number of digits to the right of the decimal point (mantissa) that should be expressed in the answer equals the number of significant digits present in the number of which the log is being taken.

Antilogarithms

The number of digits expressed in the answer (those to the right and left of the decimal point) equals the number of significant digits present in the mantissa of the number of which the antilog is being taken.