1. The Five Important Principles
Decimals
The Five Important Principles

2. Principle One
Decimals extend the place value system to represent parts of the whole.
Write four ones and two tenths as a decimal.
4.2
Write six ones, four tenths and two hundredths as a decimal.
6.42
Why do we need a decimal before the 10ths place?
Otherwise 2.0 would look like 20.

3. Principle Two
The base ten place value system is built on symmetry around the ones place.
Draw an example of a line of symmetry on your white board.
ths 100ths
line of symmetry

4. Principle Three
Decimals represent parts of a whole, whole numbers and mixed numbers.
Write 0.32 as a fraction.
32/100
Write 3.2 as a mixed number
3 2/10
Write 3.2 as an improper fraction.
32/10
Write 3.0 as an improper fraction and whole number
30/10 or 3

5. Principle Four
Decimals can be interpreted and read in more than one way.
On your white board, find different ways to show the decimal 3.2

6. Principle Five Decimals can be renamed as other decimals or fractions.
Using your white board or chart paper, shade 20 squares out of a hundred square grid.
Describe as:
Three fractions
20/100 = 2/10=1/5
Two decimals
0.20 and 0.2

7. 0.2 and 0.20 Are these decimals equivalent?
Yes, because 20/100 and 2/10 are equivalent
Yes, because 0.2 equals 2 tenths and 0.20 equals 2 tenths and zero hundredths.
In measurement we must be more precise though and use more decimal places. There is a lot of difference between 3.20 metres and 3.2 metres when you are building a bridge! The more decimal places, the more precise the measurement.

8. Equivalent Fractions and Decimals
Find the decimal equivalent:
0.5 or 0.50
0.25
1/8
0.125
How did we do this?
Find the decimal equivalent of 1/3 by dividing the denominator into the numerator.
This is a repeating decimal.
Why does it repeat?
We show this by placing a line over it.