1. Converting a repeating decimal to a fraction

2. Vocabulary –Shoot For The Stars 30 seconds
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Vocabulary –Shoot For The Stars seconds
I got this! I know this word AND I could even teach it to somebody else.
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3. ESSENTIAL QUESTION: Why is a repeating decimal a rational number
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Vocabulary
Repeating Decimal - a decimal in which a figure or group of digits is repeated in a pattern forever, as in 0.333…
Variable - A symbol for a number we don't know yet. It is usually a letter like x or y.
Equation – A statement indicating the equality of two expressions. It is split into left and right sides joined by an equal sign.

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6. Recurring Decimals They are ‘rational numbers’
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
All recurring decimals can be written as fractions. In other words, you can write it on a piece of paper using a bar.
They are
‘rational numbers’

7. As a fraction on a piece of paper, it is
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
Since you can write
A recurring decimal
As a fraction on a piece of paper, it is
Rational.

8. ESSENTIAL QUESTION: Why is a repeating decimal a rational number
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
To write recurring decimals as fractions, we use a simple multiplying method called…
Ten Again Ten

9. ESSENTIAL QUESTION: Why is a repeating decimal a rational number
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
To do so, you keep multiplying by 10 until the ending part of the decimals are the same …

10. Recurring Decimals e.g. 0.333333333… Let x = 0.333333333…
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
e.g …
Let x = …
Keep multiplying by 10 until the ending part of the decimals are the same …
Sooooo 10x = …

11. Recurring Decimals Then…
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
Then…
Subtract the two variable expressions that contain similar decimal endings.

12. Recurring Decimals 10x = 3.33333333… - x = 0.33333333… 9x = 3
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
10x = …
- x = …
9x = 3
X = 3 = 1

13. Recurring Decimals e.g. 0.565656… Which two have similar endings?…
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
e.g …
Let x = …
10x = …
100x = …
Which two have similar endings?…

14. Recurring Decimals Now Subtract 100x = 56.56565656… - x = 0.565656565
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
Now Subtract
100x = …
- x =
99x = 56
X = 56 99

15. Recurring Decimals Reminder:
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Recurring Decimals
Reminder:
Recurring decimals are written by using a bar:
e.g …. = 0.3
e.g …= 0.847

16. Now you try Convert the decimals to fractions 0.545454….. 0.599999….
ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?
Now you try
Convert the decimals to fractions
….. …. ….
0.222…