**Significant figures** are critical when **reporting scientific data** because they give the reader an idea of how well you could actually **measure/report** your data. Before looking at a few examples, let's summarize the rules for significant figures.

- ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are
**ALWAYS**significant. - ALL zeroes between non-zero numbers are
**ALWAYS**significant. - ALL zeroes which are
**SIMULTANEOUSLY**to the right of the decimal point AND at the end of the number are**ALWAYS**significant. - ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are
**ALWAYS**significant.

A helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.

# Examples: How many significant figures are present in the following numbers?

# Addition and Subtraction

When adding or subtracting numbers, count the **NUMBER OF DECIMAL PLACES** to determine the number of significant figures. The answer cannot **CONTAIN MORE PLACES AFTER THE DECIMAL POINT THAN THE SMALLEST NUMBER OF DECIMAL PLACES** in the numbers being added or subtracted.

# Multiplication and Division

When multiplying or dividing numbers, count the **NUMBER OF SIGNIFICANT FIGURES**. The answer cannot **CONTAIN MORE SIGNIFICANT FIGURES THAN THE NUMBER BEING MULTIPLIED OR DIVIDED** with the **LEAST NUMBER OF SIGNIFICANT FIGURES**.