How do you place 0.2, 0.22, 0.222, 0.2222, and 0.22222 on a number line? Thank you!
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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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Place it in this order. Least to greatest. Left to right.
- 0.2
- 0.22
- 0.222
- 0.2222
- 0.22222
0.2, 0.22, 0.222, 0.2222, and 0.22222
0.2, 0.22, 0.222, 0.2222, and 0.22222
This is already in order from least to greatest so you can write that as is on the number line. Granted, the spacing between the first two numbers will be significantly larger than the last two numbers because the numbers are merely increasing by small factor.
0.2, 0.22, 0.222, 0.2222, and 0.22222 these are already in order of least to greatest, the first 2 numbers are going to have a bit more distance than the others, then as your proceed to add the other points the distance will become smaller and smaller
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