Final answer:
Counting numbers are exact whole numbers greater than zero, used in quantifying objects exactly during the counting process. They form a part of our base-ten numerical system which is universally accepted regardless of cultural or geographical differences.
Step-by-step explanation:
Counting numbers are considered whole numbers greater than zero, used for the purpose of quantifying objects in a one-to-one correspondence. They are considered exact numbers, as the quantity they represent is definite and does not change during the counting process, unlike measured quantities that can have a degree of uncertainty. For instance, when you count the number of phone calls you receive over the course of a week, you might count zero, one, two, or three for each day, and this count is an exact number.
The counting system we use is based on the powers of ten, reflecting the number of digits in our hands, and each digit in our system represents a tenfold increase from the one to its right. The digits 0 through 9 form all of the numbers we use in counting, with the decimal point assumed to be to the right of the last digit if not shown, as in 123 representing 123. The notation we use follows a pattern based on the base-ten system due to this counting method's historical origin.
Exact numbers include integers obtained from counting objects directly, such as counting eggs in a carton, and numbers defined by quantities, like 1 foot being exactly 12 inches. Measured quantities, in contrast, often have uncertainties depending on the precision of the measuring tool and are not considered exact numbers. Counting provides a completely precise number assuming the quantity being counted does not change.