Arithmetic, error, numerical methods, TV, artifacts in the images

Lulu asked me if 10 divided by 3 is 3.333 (where the underline means repeating 3 forever). I said yes, but a computer can't do that because it has finite memory. And I explained that because a computer can't do that, there's always error, a difference between the result the computer gives and the actual answer. And I mentioned that we humans don't have that problem. She asked why.

I explained that we can think in terms of 1/3rd. So like 10 divided by 3 is 3 and 1/3rd. And I explained that a computer can't do that. I also clarified, "well at least some software can't do it, maybe some software can."

I explained that computer software implements numerical methods designed to reduce the error. 

I explained geometric growth of error versus linear growth of error. I said something like: 

• imagine a computer program that does some calculations and the error adds up (the same amount per calculation -- i.e. linear growth of error), and imagine a computer program that does some calculations and the error multiplies up (the error amounts per calculation go up with each calculation -- i.e. geometric growth of error). I said that geometric growth of error can produce results with error greater than the results.

I explained that TVs use these numerical methods and that the errors are things that you can see in the images. Like when an object is moving fast across a background, you can see artifacts in the border between the moving object and the background. Those artifacts are the errors. She asked me to show her these things. I said that I'll point it out the next time we watch something where there's an object moving fast across a background.

I explained that TVs need to use numerical methods because they don't directly show you the video feed they get. Like the video feed might have a lower frame rate than the TV will display, so the TV creates extra frames from the video feed frames.