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Significant figures or significant digits is a system for keeping track of the precision of a calculation. For example, if I have 1/3 of a Pizza, and I need to divide that pizza between 4 people, I'd need 1/12 of the pizza for each person.
However, sometimes we have to round our answers (e.g. when entering the values in a calculator or computer). Using the above example, if we used 0.33 for 1/3 and 0.25 for 1/4, then we have two decimal places of precision, or two significant digits after the decimal place. Multiplying those two values gives 0.0825. Since we know only two of our digits in each of the multiplying numbers were accurate, we can only assume that two of the digits in the answer is correct.
As an illustration, consider that 1/12 is really 0.0833333... As you can see in this case, the first two digits (0.08) are correct, and the subsequent digits are incorrect.
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