A system designed to allow an author to tell the reader how precisely they were able to measure data.

Helpful information:

All measured data has some degree of estimation. The only exception being small counted numbers (like 24 apples. We can count 24 hours without estimating.) Counted numbers really have infinite sig figs.

Sig Figs: All the digits the author is certain of plus one uncertain digit.

Example: If you use a ruler to measure the length of a string but your ruler only has centimeters, not millimeters, you can only be CERTAIN of the centimeter. But you can ESTIMATE the millimeters. So if the string is between 3 and 4 centimeters, you can se 3.5 or 3.6. Because the readers know only one digit can be uncertain, they know it must be between 3 or 4 centimeters, but the 5 and 6 millimeters are just estimated.

Zeros have special rules:

• Captive zeros: 0s that are sandwiched between other numbers (such as 506) are significant. (so 506 has three significant figures)

• Leading zeros: 0s placed on the left on non-zeros. (such as .000678) are placeholders and are not significant. (so .000678 has three significant figures)

• Trailing zeros: 0s on the right side of the non-zeros (such as 749000 or 74900.00 are only significant if the number contains a decimal point. (so 74900 only has three significant figures because there is no decimal, but 74900.00 has seven significant figures because there is a decimal point)

Multiple/Divide rules:

When multiplying/dividing sig figs, the answer can only have as many sig figs as the data with the fewest sig figs.

Example: When dividing 32.02/0.17, the calculator will say 188.352941 or 1.88352941 x 10^2. But because 0.17 only has two significant figures, the answer can only have two significant figures and can be rounded to 190 (because there is no decimal the 0 is not significant) or 1.9 x 10^2. This is because if you say the answer is 188.352941 then the reader will assume that you have measured all of those decimal places correctly and they aren’t estimated. But you didn't measure that far, you only measured to the hundredths place, so it would be spreading incorrect information.

Add/Subtract rules:

When adding/subtracting sig figs, the answer can only have as many decimal places as the data with the fewest decimal places.

Example: when adding 37.12 + 1.5 + .237 the calculator will say 38.857 But because 1.5 only has one decimal place, the answer needs to be rounded to 38.9. This is because if you say the answer is 38/857 then the reader will assume that you have measured all of those decimal places correctly and they aren’t estimated. But you didn't measure that far, you only measured to the tenths place, so it would be spreading incorrect information.