What do I call a number that has a period in it?

Question

My brain is standing completely still on this. I'm sure I've known this in the past. The difference between the number:

123

and

123.25

is obviously that the first number number is a "full" number. There is no fraction of a number that requires that the number be written with a period symbol and more numbers describing the fraction.

What is a number called when it can be written without a period, and what is it called otherwise? Also, what are the numbers behind the period symbol called? (So really this is a request for three words, not one. I hope that flies.)

Answer 1

1. Counting numbers = {1, 2, 3, ...}
2. Whole numbers = {0, 1, 2, 3, ...}
3. Natural numbers is often synonymous with counting numbers. But the term is sometimes used to mean whole numbers.
4. Integers = {..., -3, -2, -1, 0, 1, 2, 3, ...}
5. ½ is an example of a fraction. 1½ is an example of a mixed number and specifically a mixed fraction.
6. 123.25 is also an example of a mixed number, specifically a mixed decimal, and usually just called a decimal number or simply a decimal.
7. 123.25 is also an example of a rational number. It can be written as a ratio (hence, rational) of two integers. Both ½ and ⅓ (which has a repeating decimal) are rational for the same reason.
8. π (pi, 3.1415...) (which has an infinite, non-repeating decimal part) is an example of an irrational number. It cannot be written as a ratio of two integers. While the fraction 22/7 is often used to do so, it is only an approximate representation.
9. Real numbers comprise both rational and irrational numbers.
10. Imaginary numbers are those numbers which are not real. Complex numbers are those that have both real and imaginary components. Consequently, all numbers, real or imaginary, can be represented as complex numbers.

The part before the decimal point is a numbers integral (or integer) part and after it is its decimal part. In terms of mathematical terminology, the before and after parts are sometimes referred to as the characteristic and mantissa respectively. As Wiktionary states, these two terms are often required when working with logarithms.

Answer 2

The first one is called a natural number (if it's positive) or an integer (if it's either positive or negative), the other one is often called a rational number (if the decimal string terminates or repeats in a pattern) or a real number (if there is no restriction on how long or regular the decimal string is). To the left of the decimal is the integer part and to the right of the decimal is the fractional part.

Answer 3

mixed decimal - a combination of a whole number and decimal, such as 59.8, 810.85

For some, that's as opposed to a decimal fraction, defined there by thefreedictionary as a decimal having no digits to the left of the decimal point except zero, such as 0.2 or 0.00354

Others, such as Merriam-Webster (and me!) define a decimal fraction as

a fraction (as .25 = 25⁄100 or .025 = 25⁄1000) or mixed number (as 3.025 = 325⁄1000) in which the denominator is a power of 10 usually expressed by use of the decimal point. [italics mine]

Answer 4

A number with no decimal values is called an integer.

If there are a limited number of decimal digits or it contains an infinite set of repeating digits, it is a rational number. If there are an infinite amount of decimal digits, it is an irrational number. The set of rational and irrational numbers are real numbers.

If there is a decimal point, the numbers to the left are the integer part and the numbers to the right are called the fractional part.