Significant Figures

AKA: Sig Figs

During the experimental process scientists collect large amounts of data and most of this data comes from measurements and calculations. Therefore, a system is needed to show the precision of their data and calculations.

The rules for significant figures is that system.

By using significant figures and following a few simple rules a scientist can include the precision of the tools used and then maintain the integrity of the data while doing calculations.

There are two types of quantities in data collection:

• Exact numbers - result from counting objects or from defined values like 2.54 cm = 1 in.
  
• Measured numbers - are inexact numbers and required a judgement call to determine.

Measured numbers should reflect all the certain digits plus the first uncertain digit. If a tool is graduated by tenths then the digits in the measurement need to show all the digits to the tenths place (±0.1) plus one uncertain digit (±0.01). Therefore, the precision of this tool is ±0.01 units.

The uncertain digit is a judgement call made by the person taking the measure-ment. All the digits before that would be certain digits because they can actually be determined by the tool being used.

A meter stick divided into millimeters will have a precision of ±0.0001 meter. All of the digits up to and including the ten thousandths place are considered significant. So, any measurements made with this meter stick should reflect this precision.

But, not all measurements will have the same precision because of the different tools used in the experimental process. So, if there is a variety of data that will be used in calculations the results must be limited to the least precise measurements.

Significant Figure Rules

Recognizing Significant Figures (sig figs)

1. All non-zero digits are significant. (1, 2, 3, 4, 5, 6, 7, 8, 9)
2. All zeroes between significant figures are significant. (1009)
3. Leading zeroes are never significant. (0.0003240)
4. Trailing zeroes are significant only if after a decimal point and following a significant figure. (0.0003240)
5. Trailing zeroes between significant figures and a decimal point are significant figures.

Examples:

225 has 3 significant figures (Rule #1)

10,004 has 5 significant figures (Rule #2)

0.0025 has 2 significant figures (Rule #3)

0.002500 has 4 significant figures (Rule #4)

3400. has 4 significant figures (Rule #5)

Calculating with Significant Figures (sig figs)

1. When adding or subtracting use the least precise place value to determine the significant figures.
2. When multiplying or dividing use the number of significant digits in the value with the fewest significant digits.
3. Don't use counting numbers for determining significant figures.
4. Don't use numbers from definitions for determining significant figures.

Examples:

225.0 + 1.453 = 226.453 = 226.5 (Rule #1)

(1.256)(2.42) = 3.03952 = 3.94 (Rule #2)

Practice

Practice is the number one thing that you can do to master significant figures but this is a skill well worth the effort. So, practice.

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