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Significant Figures: Addition and Subtraction

Significant Figures: Addition and Subtraction

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

When adding or subtracting,

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. 

Adding and Subtracting

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.

 

http://sophia.org/packets/552