Basic Statistics > Significant Digits

Overview of Significant Digits

Significant digits (also called significant figures) refers to how many important or interesting digits there are in a number. For example:

• 323 = 3 sig. digits
• 3232 = 4 sig. digits
• 3,000.1 = 5 sig. digits
• 0.0035 = 2 sig. digits. We aren’t ever interested in leading zeros.

Trailing zeros

Trailing zeros have some ambiguity to them. Sometimes they are important, sometimes they are not. There are a couple of general rules to remember.

• 3,000 = 1 significant digit. We generally aren’t interested in trailing zeros, because we don’t know anything about the zeros (this could be a rounded number). But, if you know it’s an accurate measurement (perhaps because you measured it exactly yourself), then it’s 4 significant digits.

*but*

• 0.030 = 2 significant digits. If you see a last zero after a decimal point, it implies it has been measured the that degree of accuracy, and 323.0 = 4 significant digits for the same reason.

Rounding in Statistics

Rounding means to shorten a number to a certain amount of significant digits. Let’s say you wanted to divide 50 slices of pizza by 6 people. If you use a calculator, you’ll get 8.33333333333. This number is pretty useless in the real world. Instead, you’ll want to round to a couple of places: 8.4. Why? Because the largest number you’re dealing with is 50, and that number has two significant digits.

Rounding Rule for Multiplying and Dividing

Take the largest number and round to that number of significant digits. For example:
1987 / 454 = round to four places
23/6 = round to two places

Rounding Rule for Roots and Powers

Do not round — you should have the same number of places as your original number. For example:
√324.34 = 5 places
2.3² = 2 places

General Rounding Rule for Statistics

In general, you shouldn’t worry too much about rounding when you report your results in statistics (for example, the mean or standard deviation). However, some authors suggest that you round to one more decimal place than the least precise number. For example, if you have 2, 4.3, 11.2, 3, 4.5, then round to one decimal place (the whole numbers are the least precise with zero places).

How to Round a Number

Draw a line where you need to round. If the first digit after the line is 0 to 4, round down and if it’s 5 to 9, round up.
Example: Round 4.866 to three places.
Step 1: Draw a line cutting off the third place: 4.8|66.
Step 2: Round the first digit after the line up or down. the first digit is a 6, so round up and remove any numbers after that place: 4.87.

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