The Decimal Repeater

Mastering the Algebra of Infinite Decimals

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Step 1: Assign a variable

Let's start by letting our decimal be represented by $x$. Write the expanded form including 2 repetitions.

$x =$ ...

Step 2: Create a pair

Multiply by powers of 10 ($10, 100...$) to align the decimal parts.

$x =$
?
$x =$
?

Step 3: Subtract the Equations

Subtracting cancels the infinite repeating part! What remains?

$x =$

Step 4: Solve for x

Write the equation as a fraction:

$x =$
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DECIMAL POINT

Teacher's Insight:

"Use the jump buttons to shift the decimals. The goal is to make everything after the decimal point match exactly!"

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Quality Education: Developing algebraic fluency to translate between numerical representations.