Exploding Dots

8.3 Adding and Subtracting Decimals

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Performing addition and subtraction with decimals in a \(1 \leftarrow 10\) machine is no different from performing addition and subtraction in a \(1 \leftarrow 10\) machine without decimals.

 

For example, here is a picture of \(22.37+5.841\).

We see the answer \(2|7.11|11|1\). Just add left to right and don’t worry about explosions!

With explosions we obtain an answer that society understand. We get 28.211. (Check this!)

 

And here is \(10.23-4.57\).

We see the answer, after some annihilations, as  \(1|-4.-3|-4\) . (Do you see this?)

Now with some unexplosions, we can fix up this answer for society to read. We get \(10.23-4.57=5.66\). (Check that you follow this.)

 

Here are some practice questions you might, or might now, want to do.

 

11. What is \(0.05+0.006\)?

      What is (0.05-0.006\)?

      Can you see the answer with dots-and-boxes? 

 

12.  Agatha says that computing \(0.0348+0.0057\) is essentially the same work as computing \(348+57\) in whole numbers. Do you agree?

Percy says that computing \(0.0852+0.037\) is essentially the same work as computing \(852+37\) in whole numbers. Do you agree?

 

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