- 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 divide one decimal by another decimal, we use long division. Don't you just love making use of existing skill sets?

First, a quick refresher on the names for the different parts of a division problem:

• The **dividend** is the thing being divided up. The "dividee," if you will.

• The **divisor** is the thing that performs the dividing. Just remember that this word sounds like "operator" or "actor"; the one who operates or acts. And what a smooth operator he is, too.

• The **quotient** is the answer. Don't get excited - not to the meaning of life, just to a long division problem. Sheesh, way to jump the gun there.

16.12 ÷ 4 = 4.03 ← quotient

↑ ↑

dividend divisor

First, let's talk about what happens when we divide a decimal by a whole number. In this case, we put the decimal point for the quotient directly above the decimal point in the dividend...

...then perform long division...

...and that's it! Decimal point, set, match!

If we have a decimal divided by something that *isn't* a whole number, we have to do slightly more work. Oh, relax. It builds character.

Example: 4.08 ÷ 3.4 = ?

First, write this division problem as a fraction:

Now multiply by a cleverly disguised form of 1:

This means that 4.08 ÷ 3.4 and 40.8 ÷ 34 will give us exactly the same result. Since 40.8 ÷ 34 is a decimal divided by a whole number, we can now work this out with long division. Two heads may be better than one, but one decimal is definitely better than two.

= 1.2

In general, if we have a division problem where the divisor isn't a whole number, we have to do three things:

1. Convert it to a new division problem where the divisor is a whole number.

2. Find the quotient for the new division problem.

3. Floss. This last one isn't directly related to division, but it's still very important.

To find the new division problem, we multiply by a cleverly disguised form of 1. This means we multiply both the dividend and the divisor by 10. We keep doing that until we have a division problem where the divisor is a whole number. Hopefully you won't have to do this so many times that you miss dinner. It's lasagna night.

Since multiplying a decimal number by 10 means moving the decimal point one place to the right, there's a nice way to summarize what we do to divide one decimal by another:

Count the number of decimal places in the divisor. Move the decimal point that many places to the right in the divisor, and that many places to the right in the dividend also. This produces a new division problem where the divisor is a whole number, and where the quotient is the same as the quotient in the original division problem. Everything stays the same, and everyone seems happy. Just like life in the suburbs.

Example 1

Solve 121.77 ÷ 1.23. |

Exercise 1

Solve 6.93 ÷ 3.

Exercise 2

Solve 7.88 ÷ 4.

Exercise 3

Solve 1.31 ÷ 2.

Exercise 4

Solve 0.75 ÷ 0.0005

Exercise 5

Solve .

Exercise 6

Solve .

Exercise 7

Solve .

Exercise 8

Solve 1.92 ÷ 0.24