Goals

To learn to determine the number of significant figures in a number

To use significant figures correctly in calculations.

To learn to use scientific notation

Determining the number of significant figures (S. F.) in a number

Measure numbers always contain error. Numbers obtained by counting or defined numbers are exact. For example 28 students is exact. 12 inches in one foot is defined and is also exact. An exact number has an infinite number of significant figures. The number of significant figures in a measured number is limited by the measuring device used
 

Rules for Counting Significant Figures:	Example	# S. F.
1. All nonzero integers are significant.	421.1	4
2. Leading zeros are never significant.	0.0034	2
3. Captive zeros are always significant.	205	3
4. Trailing zeros in a decimal number are significant.	25.0	3
5. Trailing zeros in a number with no decimal are not significant.	400	1

Exponential Notation:

The number of significant figures in a number written in exponential notation is easily determined as the leading and trailing zeros are removed.

Examples:
 

Decimal	Exponential notation	# S. F.
0.0034	3.4 x 10 ¾ 3	2
400	4 x 10 2	1
0.000505	5.05 x 10 ¾ 4	3
530000	5.3 x 10 5	2
0.0100(0.0100 contains trailing zeros within a decimal.)	1.00 x 10 ¾ 2	3

Rules for Rounding:

In a calculation carry all of the significant figures through to the final result, then round.

1. If the digit to be removed is <5, the preceding digit remains unchanged. 25.44 rounds to 25.4.

2. If the digit to be removed is >= 5, then the preceding digit is incremented by 1. 25.46 rounds to 25.5.