- 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

To add decimals, remember that decimals are abbreviations for fractions.

0.3 + 0.04 + 0.001 translates to .

Since and , this means that .

Is this paragraph making you dizzy? Well, stop running in circles, sit down, and for goodness' sake, eat something!

The example in the previous paragraph represents the long way to do things. (Sigh of indescribable relief.) While it's mathematically correct to turn decimals into fractions, add the fractions, then turn them back into decimals, it's too much work. Solving decimal problems that way would be like deleting all your songs on iTunes and then uploading them again just so you can change the order of your playlist. By the way, *David Hasselhoff Sings America*? Really?

Instead, remember that adding zeros to the end of a decimal doesn't change its value, so 0.3 = 0.300. (This is the same as saying but without having to write the fractions.)

Also, we can rewrite the 0.04 part of the problem as 0.040. The last part, 0.001, is already written out to the thousandths place, so we can leave that one alone. Good thing, because all this decimal manipulation is wiping us out.

To add up the decimals, always add zeros to the ends of the decimals as needed so that all of them have the same number of decimal places (like we did above). Line up the numbers at the decimal point, and add them like whole numbers:

0.300

0.040

+ 0.001

= 0.341

We're really adding up just like we did before, but without having to write the fractions. Good thing, because all this fraction writing is wiping us out. In hindsight, maybe we just didn't get enough sleep last night.

Subtraction is similar. To subtract one decimal number from another, first give the two decimals the same number of decimal places by adding zeros at the end as needed. Line up the numbers at the decimal point, and then carry out the subtraction as you would with whole numbers. If you have a different, "cool" way of subtracting whole numbers, then never mind.

Example 1

Solve 0.5 + 0.94 + 0.032. |

Example 2

Solve 0.223 - 0.101. |

Example 3

Solve 0.1803 - 0.09. |

Exercise 1

Solve 0.456 + 0.231.

Exercise 2

Solve 0.02 + 0.3107

Exercise 3

Solve 0.876 - 0.135

Exercise 4

Solve 0.96 - 0.004