Significant Figures

General Rules

Examples

• 30525 has five significant figures, four non-zero digits, and one zero between non-zero digits. 
• 0.236 has three significant figures, one non-significant trailing zero that does not count towards the number of significant figures, and three significant non-zero digits. 
• 56.00 has four significant figures, two non-zero digits, and two trailing zeros to the left of the decimal. 
• 320. has three significant figures because of the decimal at the end of this whole number shows the trailing zero is significant
• 2500 has two significant figures. Two non-zero digits that are significant and two non-significant trailing zeros. Since there is no decimal at the end of those trailing zeros they become non-significant. 
• Numbers that are definitions such as 1 km have infinite significant figures. 
•  5.02 x 10⁴  has three significant digits, because of 5.02, 10⁴ is non-significant based on the above rules. 
• 55.62 has four significant figures because all the non-zero numbers are significant

Math with Significant Figures

Rounding a Number

When rounding off a number to keep only the amount of significant figures you need use the following rules

• If the number you want to round is followed by 5 or any number greater than five (6,7,8,9) round the number up by one. 
• If the number is followed by a number less than five (0,1,2,3,4) then round the number down. 

1 . Addition and Subtraction

• Count the number of significant digits after the decimal
• Add or subtract the numbers
• The round the final answer to the least number of places in the decimal part of any number

Example I

2.550 + 3.5001 = 6.0501 (We are not done yet!)

• 2.550 has three digits after the decimal
• 3.5001 has four digits after the decimal
• 2.550 has the least number of digits after the decimal

Therefore the answer should have three digits after the decimal. The fourth number is one. Since it's less than five we should round down the final answer to 6.050 

Example II

52.36095 - 32.232 = 20.12895

• 52.36095 has five digits after the decimal
• 32.232 has three digits after the decimal
• 32.232 has the least number of digits after the decimal

Therefore the answer should have three digits after the decimal. The fourth number is nine. Since it's greater than five we should round up the final answer to 20.129 

2 . Multiplication and Division

The significant figures in the result, for both multiplication and division, are determined by the least number of significant figures in any number. 

Example I

An object has a mass of 35.5324 g and a volume of 15.0 cm³, then find the density.

15.0 cm³ has the least number of significant figures (three significant figures), therefore the answer has three significant figures.