How do you place 0.2, 0.22, 0.222, 0.2222, and 0.22222 on a number line?

Expert Answers

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They're already in increasing order, which is obvious. If you want to "prove" it (in quotes because the fact may be considered so basic as to not need proof), you can always write the numbers with a common denominator as

`20000/100000<22000/100000<22200/100000<22220/100000<22222/100000,`

but that may be overkill. Anyway, they go left to right in the order you wrote them. However, the distance between two consecutive numbers keeps getting smaller. In fact, it gets 10 times smaller each time. So 0.222 is 10 times closer to 0.22 as 0.22 is to 0.2, and so on. Let's see if I can plot single points...

At this scale, the last 3 points are practically indistinguishable. To clearly make out every single point, you would have to work on a number line scaled so that 0.2 and 0.22 are about 10 feet (roughly 3 meters) apart. Then the last two points would still only be about an eight of an inch (roughly 3mm) apart.

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