- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
**Decimals**- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
**Infinite Decimals**- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

So far, all the decimal arithmetic we've done has involved decimal numbers with a finite number of decimal places. However, sometimes decimal numbers are infinite. Make sure you don't confuse "infinite decimal" with "infinitesimal." Although a number can sometimes be both, they're not the same thing. Even though they sound *exactly* the same when pronounced aloud. Thanks again, English.

**Infinite decimals** sometimes show up when we convert fractions into decimals.

**Sample Problem**

Convert the fraction 1/3 into a decimal, using long division:

We end up with a decimal that goes on forever. Literally. And we thought Mondays seemed long.

To show an infinite decimal, we write "..." at the end. This is also good for when you get bored writing all the digits of a lengthy finite decimal, or when your pen is running out of ink.

0.33333333...

Another way to write an infinite decimal with a repeating pattern is to draw a bar over the part that repeats.

_

0.333333333.... = 0.3

(On a side note, if one bar isn't enough and you wanted to completely cage in that 3, you could make him the numerator in a fraction and take the absolute value: . There. He's not going anywhere *now*.)

There are also infinite decimals *without* repeating patterns. These decimals represent the irrational numbers, and there is no way to know all the digits of any such number. And please don't take that as a personal challenge. We don't want to see you wasting the next thirty years of your life trying to memorize pi to an infinite number of digits before finally realizing it can't be done. We'd feel partly responsible.

However, you *can* see at least the first few digits of some famous infinite decimals:

Example 1

Please divide 9/11. |

Exercise 1

Convert the fraction into an infinite decimal.

Exercise 2

Convert the fraction into an infinite decimal.