pdf Convert Repeating Decimals To Fractions

This worksheet provides a clear, step-by-step method for converting repeating decimals into fractional form. Students are guided through the algebraic process of rewriting a repeating decimal as a variable, multiplying by powers of ten, creating two equations, and subtracting to eliminate the repeating portion. This structured approach helps students understand not just how to convert, but why the method works.

The included example models the full procedure using a repeating decimal such as \(0.04666\ldots\). Students learn to set the value equal to \(x\), write equations such as \(100x = 4.666\ldots\) and \(1000x = 46.666\ldots\), subtract to eliminate the repeating portion, and solve for \(x\) to obtain a simplified fraction. After working through the modeled example, students convert a variety of repeating decimals—including single-digit repeats like \(0.\overline{3}\) and multi-digit repeats such as \(0.\overline{12}\) and \(0.\overline{836}\)—into their fractional equivalents.

Because this resource blends algebraic reasoning with number sense, it works well as guided instruction when introducing repeating decimals, independent practice to reinforce the subtraction method, or review before classifying rational and irrational numbers. The variety of examples ensures students develop confidence with both simple and more complex repeating patterns.

Skills Assessed

• Converting repeating decimals to fractions

• Writing algebraic equations to represent repeating decimals

• Using powers of ten to shift decimal values

• Eliminating repeating portions through subtraction

• Simplifying fractions to lowest terms

• Strengthening understanding of rational numbers

Details

• 2 pages

• Answer key included

ID# 0651