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What is a Real Number?

Author: Michael Morgan

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-  http://www.mathsisfun.com/numbers/real-numbers.html

Terminating Decimal- http://www.icoachmath.com/sitemap/terminating_decimal.html

Rational Numbers- http://www.mathsisfun.com/rational-numbers.html