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# 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 * 102. To write 200 with 3 significant figures, it would be written 2.00 * 102.

• 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.

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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