Every measurement or calculation we do with instruments in chemistry has some level of uncertainty called *experimental error*. Significant figures are necessary to communicate a level of accuracy and precision while dealing with this uncertainty.

**Rules for Number of Signficant Figures**

__Rule 1__: If your number has a ** decimal point** move from

*Trailing zeros* are a sequence of zeros after the decimal point once you’ve passed all non-zero integers. They would be significant.

__Rule 2: __If your number has ** NO decimal point** move from

If a value has no decimal point then the final zero would mean it has an infinite number of significant figures.

**Exact Numbers **

Exact numbers contain an infinite number of significant figures because they represent the amount of a particular item and not a measurement.

For example, when we say that a decade is equal to 10 years, there are 150 students in your chemistry class, or NH_{3} contains 1 atom of nitrogen and 3 atoms of hydrogen.

**Addition & Subtraction**

When dealing with addition or subtraction the least number of decimal places will determine the final answer.

^{6}, but the final answer should have only 1 decimal place and so the answer is rounded. Adding the two values gives the initial value of 5.375 x 10

**Multiplication & Division**

When dealing with multiplication or division the least number of significant figures will determine the final answer.

Multiplying the two values gives an initial value of 103.6, but you must round your final answer to significant figures.

Furthermore keep in mind when dealing with mixed operations we must follow the same arithmetic guidelines as we always do.

**Logarithm & Natural Logarithm**

When taking the (log) or (ln) of a value, the number of significant figures it has determines the number of digits ** after** the decimal point for the answer.

Using your calculator, the log of 1.53 x 10^{-3} gives an initial value of - 2.01531. The value of 1.53 x 10^{-3} has 3 significant figures and so the final answer should have 3 digits after the decimal point.