SOLUTION: 101/102 or 1001/1002? determine which one is bigger. Give at least three explanations for each pair: one contexual, one a picture, and other explanation for your choice. I was able

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Question 520860: 101/102 or 1001/1002? determine which one is bigger. Give at least three explanations for each pair: one contexual, one a picture, and other explanation for your choice. I was able to draw out the pictures but i cannot explain the rest. Please help!
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

I suppose for a "contextual" explanation you could simply do the divisions on a calculator and see which is the larger. If you aren't sure which is which, subtract one decimal fraction from the other. If you have subtracted the smaller from the larger, you get a positive result.

You could also just subtract the two fractions:

So the 4 digit fraction is the larger.

The following is a rigorous proof:

Since

and

we can say

and

Since

Then we are certain that since

we can be certain that

Hence

and then, by substitution:

and finally, subtracting out

John

My calculator said it, I believe it, that settles it