Question

Why isn't ones place not there in decimal part of decimals?

Answer 1

Let's think about it a moment: What are "oneths"? A "oneth" would be 1/1, so there already is a "oneths" place. It's called the ones' place. You don't need another. As I'll explain in a moment, this is a lot like the reason there is no -0: 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, 100, and so on. On the right we have 1/10, 1/100, and so on. Shouldn't everything on the right match up with something on the left, 1/10 with 10 and so on? Or to put it another way, when we convert, say, 1/1000 to decimals, we find that although 1000 has three zeroes, 0.001 has only two! 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, 1000 has two zeroes to the left of the ones', and 0.001 has two zeroes to the right of the ones'. The 1 in 1000 is three places to the left of the ones' place, and the 1 in 0.001 is three places to the right of the ones' place. If we wrote numbers by underlining the ones' place rather than putting a decimal point after it, there would be no confusion.