Transform Recurring Decimal into Rational Number – Live Demonstration

Purpose

Transform any repeating (recurring) decimal into \( \frac{p}{q} \) form (rational number).

Format

\(a.\overline{bcd}\)

• \(x\) = No. of the digits = 3
• \(y\) = No. of the \(a\) = 1

Transformation

Let \(n = a.\overline{bcd}\)

\( n = \frac{p}{q} = \frac{10^x \cdot n - 10^y \cdot n}{10^x - 10^y} \)

Example

For \(3.\overline{579}\)

• \(x\) = 3
• \(y\) = 1

Let \(n = 3.\overline{579}\)

\( 10^3 \cdot n = 3579.\overline{579} \)

\( 10^1 \cdot n = 30.\overline{579} \)

\( n = \frac{3579.\overline{579} - 3.\overline{579}}{10^3 - 10} \)

\( n = \frac{3576}{990} \)

\( n = \frac{596}{165} \)

Transform Recurring Decimal into Rational Number - Live Demo

Number with Decimal Part

Repeating Part

Convert to Rational