Table of Contents
What is a Number System?
A number system is a way of representing numbers using symbols. There are many different number systems, but the most common one is the base 10 number system. In this number system, each number is represented by a combination of 10 symbols, 0 through 9.
Rational Numbers
Rational numbers are numbers that can be expressed as a fraction, or ratio of two integers. In other words, rational numbers can be written as p/q, where p and q are integers and q is not zero.
The most basic rational number is 1/1, which is simply the number 1 expressed as a fraction. Other examples of rational numbers include 2/1, 3/2, and 5/4.
Rational numbers can be used to measure things that are divisible by a certain unit, such as inches, pounds, or minutes. For example, if you wanted to measure the length of a room, you could use rational numbers to measure the length in inches, feet, or yards.
Irrational Numbers
An irrational number is a number that cannot be expressed as a rational number. This means that it cannot be expressed as a fraction of two integers. Irrational numbers are found in nature, and are used in many mathematical formulas.
Some irrational numbers include pi, the square root of 2, and the golden ratio. These numbers cannot be expressed as a fraction of two whole numbers, but they can be expressed as decimal values that go on forever without repeating.
Real Numbers
A number is any quantity that can be counted. The natural numbers are 1, 2, 3, and so on. The whole numbers are 0, 1, 2, and so on. The integers are the natural numbers and the whole numbers. The rational numbers are all the numbers that can be expressed as a fraction, a decimal, or a percentage. The real numbers are the rational numbers and all the irrational numbers.
Terminating Decimal Numbers
A terminating decimal number is a number that has a finite number of digits that repeat after a decimal point. For example, the number 2.75 has 2 digits that repeat after the decimal point. The number 5.00 has 5 digits that repeat after the decimal point.
A non-terminating decimal number is a number that does not have a finite number of digits that repeat after the decimal point. For example, the number 3.14159265358979323846264338327950288… does not have a finite number of digits that repeat after the decimal point.
Non-Terminating Decimal Numbers
Non-terminating decimal numbers are numbers that do not have a finite number of digits after the decimal point. They go on forever. For example, the number 0.333… is a non-terminating decimal.
There is no definitive answer as to whether or not non-terminating decimal numbers actually exist. Some mathematicians believe that they do, while others believe that they don’t. The debate is ongoing.
Recurring Decimal Numbers
A recurring decimal number is a number that can be represented as a fraction in which the numerator and denominator are both integers, and the numerator is a multiple of the denominator. For example, the recurring decimal number 0.333… can be represented as the fraction 3/9.
Rational Numbers on the Number Line
The rational numbers are all of the numbers that can be written as a fraction. This includes all of the whole numbers, all of the fractions, and all of the decimals.
The number line is a great way to visualize the rational numbers. On the number line, the rational numbers are all the numbers that are between the whole numbers. This includes all of the fractions and all of the decimals.
