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As I try to do still working at being consistent with this! And, as usual, I am glad I did. And what a discussion we had! We looked at the place value chart. We talked about what happened as we moved left and right.
You don't need another. As I'll explain in a moment, this is a lot like the reason there is no negative zero is the same as positive zero, so we only need one of them in the number line. What you're noticing is that the place values don't seem symmetrical , or balanced. On the left we have 1, 10, , and so on. Why can't it be simpler? Place values really are symmetrical. The problem is that the center is at the ones' place, not at the decimal point where we would like it to be.
If you think of the ones as being in the middle, then as you move to the left, you multiply by 10 each time, and as you move to the right, you divide by 10 each time. The trouble is caused by the decimal point: it's off-center. It was natural to put it to the right of the ones' place, to separate the fraction part of a number from the integer part, but that takes away the symmetry.
What you have to do is to think of the ones' digit as special, and count places to the left or right of that. For example, has two zeroes to the left of the ones', and 0.
The 1 in is three places to the left of the ones' place, and the 1 in 0. If we wrote numbers by underlining the ones' place rather than putting a decimal point after it, there would be no confusion. Another way to look at this is to relate place values to the number line. Each place corresponds to a power of ten: It doesn't belong on either side, but in the middle. There aren't both a positive and a negative zero, and there aren't both ones and oneths.
The ones' place, just like 0 on the number line, belongs in the middle. I hope that helps. It's interesting how we tend to expect things to be symmetrical. Mathematicians and scientists often expect it too, and when things don't seem balanced, they try to find out why.
So keep wondering about things like this. Curiosity made the mathematician! Zeros at the end, I There are several issues raised by zeros in decimal numbers.
The next question, from , is about the effect or not of zeros at the end of the number: Ignoring Zeros Here's the problem. I just want to know what to do. You have 0. My teacher says they are equal. The thing I do not understand is the number 0. Is point thousandths right or wrong?
So shouldn't 0. Or does the zero not count? I answered: Hi, Cole.
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