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# Significant Figures: Addition and Subtraction

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Author: Katie Smith
##### Description:

This packet reviews how to properly consider significant figures when doing calculations which involve addition and subtraction.

This packet includes a video explaining how to add and subtract, and practice problems for you to work on your own.

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Tutorial

## The Golden Rule

consider the Least Certain Place.

Say we have a beaker containing 5 litres of water.  You add in an extra 3 mL, and someone asks how much water you have now.  Hopefully, you answer that you still have 5 litres of water.

Huh???!?

Well, when you started with 5 litres, that had one significant figure, meaning that the 5 was a bit uncertain.  In other words, what you REALLY knew is that you had between 4 and 6 litres.  When you add in the extra 3 mL,  (remember, 5 liters would be 5000 mL, or 3 mL would be 0.003 L), you could say that you have 5.003 L.  But do you really?  To say 5.003 L would imply that you have between 5.002 and 5.004 L -- and that's not fair at all!  Really, you now have somewhere between 4.002 and 6.004 liters (that 3 was uncertain, too!).

You can't go beyond the least certain place.  You can't say you have 5.003 L when you don't even know if you started with 4 L, 5 L or 6 L.  So for our final answer, we need to stick with the ones place when writing liters, and 5.003 rounds to 5 L.

Does that make sense?  We'll look at a few more in the video below.

This video will walk through how to complete calculations involving addition and subtraction with the proper use of significant figures.

## Practice Problems

Now try these on your own!

## Now What?

Once you're comfortable adding and subtracting numbers, and reporting the final value with the correct number of significant figures, you're ready to move on to the next step:  multiplication and division.  Use the link below to move to the next topic.

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