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What is a Real Number?

What is a Real Number?

Author: Michael Morgan

The purpose of this packet is to explain what a real number is.

This packet is not going to be exciting, but it will help you. Real numbers are defined and some associated words compliment the original definition. Links to other websites are provided.

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Real numbers consist of any number that can be plotted on a number line. They can be positive, negative, integers, rational, irrational, roots, repeating decimals, non-repeating decimals, and terminating decimals. 


Things to Know

Rational number- any number that can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero. Any integer is a rational number.

Irrational number- any real number which cannot be expressed as a fraction p/q, where p and q are integers, with q non-zero and is therefore not a rational number. An irrational number cannot be written as a simple fraction. Most commonly used irrational numbers are e and pi. 

Repeating decimal- any fraction, such as 1/3, that has a continuously repeating decimal. We can represent a repeating decimal by placing a bar above the last written number or by placing 3 periods (...) after the last digit.

Non-repeating decimal- any number, such as pi, that never repeats itself after the decimal. Irrational numbers are good examples of a non-repeating decimal.

Terminating decimal- any decimal that has an end. Some examples of a terminating decimal are: .75, 3.28, .6, etc. 

Reference Sites

These are a few websites that will help in understanding real numbers and other terms mentioned above.


Real Numbers-

Terminating Decimal-

Rational Numbers-