Unit 1: Working with Decimals
Topic A: Part of the Whole Thing
This is the beginning of an adventure with numbers that represent part of the whole thing. These numbers can be shown in a few different ways:
| Fraction name | Example |
|---|---|
| Decimal fraction | 0.50 |
| Common fraction | [latex]\dfrac{1}{2}[/latex] or [latex]\dfrac{50}{100}[/latex] |
| Percent fraction | 50% |
When we talk about fractions in any of the three ways listed above, we are talking about numbers in relation to the whole thing. What do we mean by “the whole thing”? We mean one complete thing.
An example would be one full jug of juice. That is 1 whole thing.
Once someone starts taking some juice, less than the whole thing remains. Now, half of the juice is gone.The remaining amount can be written as
- half of one whole thing
- 0.5
- ½
- 50%
Now almost all the juice has been taken.
The remaining amount can be written as
- 0.25
- ¼
- 25%
Now there are two full jugs of juice. This shows two whole things.
A fraction does not tell us much unless we know what the fraction is part of—we need to know exactly what the whole thing is! If someone says to you, “Sure, let’s go! I still have half!” you really need to know, “Half of what?”
The answer could be [latex]\frac{1}{2}[/latex] a tank of gas, or [latex]\frac{1}{2}[/latex] a paycheque, or [latex]\frac{1}{2}[/latex] a vacation, or [latex]\frac{1}{2}[/latex] an hour.
Decimal Fractions
Decimal fractions are one way to consider parts of the whole thing. The whole thing = 1.
You use decimal fractions every time you think about money. The dollars are written as whole numbers and the cents are written as a decimal fraction of a dollar.
A decimal fraction has a decimal point that separates the whole number from the fraction. The decimal point looks like this:
A whole pizza might be divided into eight pieces, or ten pieces, or twelve pieces. However, for decimal fractions the whole is always divided into ten pieces, which are called tenths. This is because we use a decimal system based on the number ten (“deci” is the Latin word for ten). The tenths are also divided into ten pieces to make hundredths. And then the hundredths are divided by ten to make thousandths, and so on.
Decimal fractions are often used in our daily lives, especially for money and measurement. For example:
- The total was $12.24.
- It is 3.5 kilometres from my house to the store.
- It costs $1.99 per kilogram for apples.
- She caught a 4.8 kilogram salmon.
You will be working with decimal fractions in the first two units of this book.
Common Fractions
Common fractions are a second way we will work with parts of the whole thing.
They are written with two numbers, one above the other, with a line in between. The line may be straight, or it may be on an angle.
[latex]\frac{3}{4}[/latex] or ¾
The numerator is the top number in a common fraction. The numerator tells how many parts. The denominator is the bottom number. The denominator tells how many equal parts there ar