When working with numbers, it is important to understand how to express the precision of your measurements or calculations. This is where significant figures come in.
Significant figures, also known as significant digits, are the digits that carry meaning in a number.
In this article, we will explore the rules for significant figures and provide examples to help you better understand how to use them.
Rule #1: Non-zero digits are always significant
Any non-zero digit is always significant, meaning that it carries meaning in the number. For example, the number 243 has three significant figures, because each of the three digits (2, 4, and 3) are non-zero.
This means that the number 243 could be a measurement with a precision of three Decimal places or it could represent a calculated value with a precision of three decimal places.
Examples:
- 8.24 has three significant figures.
- 531 has three significant figures.
- 0.715 has three significant figures.
Rule #2: Zeroes between non-zero digits are always significant
When zeroes appear between non-zero digits, they are always significant. For example, the number 3004 has four significant figures, because the zeroes in the middle (between the 3 and the 4) are between two non-zero digits.
This means that the number 3004 could be a measurement with a precision of four decimal places or it could represent a calculated value with a precision of four decimal places.
Examples:
- 1002 has four significant figures.
- 0.002034 has four significant figures.
- 501.02 has five significant figures.
Rule #3: Leading zeroes are not significant
When a zero appears before the first non-zero digit in a number, it is not significant. For example, the number 0.00321 has three significant figures, because the first two zeroes are not significant.
This means that the number 0.00321 could be a measurement with a precision of three decimal places or it could represent a calculated value with a precision of three decimal places.
Examples:
- 0.023 has two significant figures.
- 0.000524 has three significant figures.
- 0.0001 has one significant figure.
Rule #4: Trailing zeroes are significant only if there is a decimal point
Trailing zeroes are only significant if there is a decimal point in the number. For example, the number 50.0 has three significant figures, because the trailing zero is after the decimal point.
However, the number 500 does not have any trailing zeroes that are significant, because there is no decimal point.
This means that the number 50.0 could be a measurement with a precision of three decimal places or it could represent a calculated value with a precision of three decimal places.
Examples:
- 12.000 has four significant figures.
- 0.400 has two significant figures.
- 305.00 has five significant figures.
Rule #5: Trailing zeroes in a number without a decimal point may be ambiguous
Trailing zeroes in a number without a decimal point may be ambiguous, meaning that it is unclear whether or not the trailing zeroes are significant.
For example, the number 5000 may have three, four, or five significant figures, depending on the context in which it is used
To avoid ambiguity, it is best to use scientific notation. Scientific notation is a method of expressing numbers as a power of ten, where the exponent indicates the number of significant figures.
Examples:
- 5.00 x 10^3 has three significant figures.
- 5.000 x 10^3 has four significant figures.
- 5.0000 x 10^3 has five significant figures.
Rule #6: Exact numbers have an infinite number of significant figures
Exact numbers are numbers that are known with complete certainty, such as the number of chairs in a room or the number of students in a class.
An exact number has an infinite number of significant figures, because it is not subject to any measurement uncertainty. For example, if a recipe calls for two eggs, the number "2" is an exact number with an infinite number of significant figures.
Examples:
- The number of pages in a book is an exact number with an infinite number of significant figures.
- The number of atoms in a molecule is an exact number with an infinite number of significant figures.
- The number of players on a basketball team is an exact number with an infinite number of significant figures.
In summary, understanding significant figures is important for properly representing measurements and calculations with appropriate precision.
By following the rules outlined above, you can determine the number of significant figures in a given number and use this information to properly round off and report your results.
Remember, when in doubt, it is always better to round to a lower number of significant figures rather than a higher number, in order to avoid overstating the precision of your measurement or calculation.
