Step 1: Assume the decimal as $x$

Let $x$ be the given repeating decimal number: $x = 6.464646...$

$x = 6.464646...$

Step 2: Multiply by $100$

Since there are two repeating digits (46), multiply both sides by $100$ to shift the decimal point by two places.

$100x = 646.464646...$

Step 3: Subtract the original equation

Subtract $x = 6.464646...$ from $100x = 646.464646...$ to eliminate the infinite repeating decimal part.

$100x - x = 646.4646... - 6.4646... \implies 99x = 640$

Step 4: Solve for $x$

Divide both sides by $99$ to get the required fractional form.

$x = \frac{640}{99}$