4.6 repeating decimals

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Slide 1: Slide

WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 14 slides, with text slides.

Lesson duration is: 50 min

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Slide 1 - Slide

Today

- I understand the differences between natural, whole, rational, irrational and real numbers.

- I understand what a repeating decimal is and know the line notation involved.

Slide 2 - Slide

I'll show you how this works.

\sqrt ​ a ​ ​ ​ \cdot \sqrt ​ b ​ ​ ​ = \sqrt ​ a \cdot b ​ ​ ​

\frac{​ \sqrt ​ a ​ ​ ​ ​ ​}{​ \sqrt ​ b ​ ​ ​ ​} = \sqrt ​ \frac{​ a ​ ​}{​ b ​} ​ ​ ​

Slide 3 - Slide

A repeating decimal

We can write this as

\frac{​ 1 ​ ​}{​ 3 ​} = 0, 333 . . .

Slide 4 - Slide

Two other examples

Slide 5 - Slide

All numbers with repeating decimals can be written as a fraction.

We can always convert a repeating decimal to a fraction using the following fun algorithm:

Slide 6 - Slide

Consider 0,99999...

Let a = 0,999...

Slide 7 - Slide

Consider 0,99999...

Let a = 0,999...

then 100a = 99,999...

Slide 8 - Slide

Consider 0,99999...

Let a = 0,999...

then 100a = 99,999...

100a - a = 99a

Slide 9 - Slide

Consider 0,99999...

Let a = 0,999...

then 100a = 99,999...

100a - a = 99a

and

99,999... - 0,999... = 99

Slide 10 - Slide

Consider 0,99999...

Let a = 0,999...

then 100a = 99,999...

100a - a = 99a

and

99,999... - 0,999... = 99

so 99a = 99 and this means

a = \frac{​ 9 9 ​ ​}{​ 9 9 ​} = 1

Slide 11 - Slide

Another example

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Slide 13 - Slide

Practice!

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Slide 14 - Slide

4.6 repeating decimals

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