Converting a repeating
decimal to a fraction
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
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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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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’
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.
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
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 …
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. 0.333333333…
Let x = 0.333333333…
Keep multiplying by 10 until the
ending part of the decimals are
the same …
Sooooo
10x = 3.333333…
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.
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 = 3.33333333…
- x = 0.33333333…
9x = 3
X=3 = 1
9
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
e.g. 0.565656…
Let x = 0.5656565…
10x = 5.65656565…
100x = 56.56565656…
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
Now Subtract
100x = 56.56565656…
- x = 0.565656565
99x = 56
X = 56
99
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. 0.3333333…. = 0.3
e.g. 0.8474747…= 0.847
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
– 0.545454…..
– 0.599999….
– 0.345555….
– 0.222…