The simplest numbers are the natural numbers:
1, 2, 3, 4, 5, ..., 9, 10, 11, 12, ..., 19, 20, ...
They are represented by using the digits 0, 1, 2, ..., 9. Each digit of a number has a place value. The last digit (when reading from left to right) has the value of the number of ones. The second to last digit has the value of the number of tens, the third to the last digit has the value of the number of hundreds and so on.
325 = 3*100 + 2*10 + 5*1.
With the natural numbers we can count. Together with their negatives and the number zero we obtain the set of integers (whole numbers):
... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
However, these are not sufficiently precise for most measurements. We often need a fraction of a number. We can represent them by using the decimal number system, which is built on base 10 arithmetic. For example, we represent
A number in decimal form has two parts separated by a dot (decimal point). The number to the left of the decimal point represents the integer part and the digits to the right of the decimal point represent successively, the number of 10ths, 100ths, 1000ths, etc. These are known as the place values.
It turns out that every (real) number on the number line can be represented in this way.
Name the place value of the given digit.
Choose the place value of the number indicated by the arrow.