# The Chemistry Tutorial - Significant Figures

When dealing with numbers in any part of Chemistry, it is important
to remember to always have the right number of significant figures,
or the number of important digits.

There are three basic rules for significant digits:

Any digit other than zero (0) is always significant

**Examples:**

4294 has 4 significant figures

29.57381284 has 10 significant figures

Zeroes in between two other non-zero numbers are significant

**Examples:**

184058 has 6 significant figures

583.029378 has 9 significant figures

4.001 has 4 significant figures

Any zero to the right of the other significant figures is
significant if and only if there is a decimal point in the
number

**Examples:**

284.9028100 has 10 significant figures

200 has 1 significant figure

Note: In order to write 200 with 2 significant figures, it
would be written 2.0 * 10^{2}. To write 200 with 3
significant figures, it would be written 2.00 *
10^{2}.

Any zero to the left of all other significant figures is not
significant

**Examples:**

0.0348 has 3 significant figures

0.00385200 has 6 significant figures

When functions are applied to numbers (addition, subtraction,
multiplication, and division), there are more rules.

**Addition and Subtraction**:

There are three parts to carrying significant
figures through to addition and subtraction.

Count the number of places to the right of the decimal point
in each number to be added of subtracted.
Carry out the addition or subtraction how it would normally be
done.
Round to the least number of decimal places counted in step 1.

**Examples:**

10.039 + 59.10584 = 69.145

0.02881 - 0.000391 = .0284

200 + 555 = 800

**Multiplication and Division**:

Count the number of significant figures in the numbers to be
multiplied or divided.
Carry out the multiplication or division how it would normally
be done.
Round to the least number of significant figures counted in
step 1.

**Examples:**

439 * 1.00382 * 27.85 = 12300

0.0290 * 1.183927589 = 0.0343

10.1 / .53923 = 18.7

39957.09 / 219.193854 = 192.2911

Lastly, there are certain numbers which are exact, meaning that they
have an infinite amount of significant figures. These tend to be
measurements, but do not have to be. For example, there are exactly
12 inches in 1 foot, exactly 1000 meters in 1 kilometer, and exactly
10 years in 1 decade. These numbers will not affect the significant
figures in a problem.

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