When looking at place values in numbers, we notice that as we go to the left, the numbers increase by a factor of 10. Each digit represents a place value that is 10 times larger than the digit to its right. For example if we look at the number 582, we can see that the 2 represents the ones place, the 8 represents the tens place, and the 5 represents the hundreds place.
If we want to represent numbers smaller than 1 using this system, we need to go further to the right than the ones place. Since every time we move to the right, we decrease the place value by a factor of 10, we say that the place value to the right of the ones place is that tenths place. Each unit here represents 1/10th.
We denote the separation of the whole numbers and the fractional portion of a decimal number by the decimal point. The decimal point is simply a period which is placed between the 1's place and the tenths place.
If we break the number above up into addition of place values we get the following:
Repeating Decimals
Sometimes with decimals we may see a pattern repeat. For example, lets say that we want to represent the number 1/3 in decimal form. The decimal form of 1/3 is 0.3333333333.... The 3's actually go on forever. In order to write this number we write it with a bar over the repeating part as shown below:
