The given number is $0.\overline{06}$, which means the decimal $0.06060606\ldots$ repeats indefinitely.

Step 1: Convert $0.\overline{06}$ into a Fraction

Let $x = 0.\overline{06}$.
Multiplying both sides by 100 (since the repeating part has two digits):
$100x = 6.\overline{06}$ Now subtract the original equation from this new equation:
$100x - x = 6.\overline{06} - 0.\overline{06}$ $99x = 6$ $x = \frac{6}{99}$ Simplify the fraction:
$x = \frac{2}{33}$

Step 2: Multiply by 100

$100 \times \frac{2}{33} = \frac{200}{33}$

Step 3: Convert to Decimal

$\frac{200}{33} \approx 6.06$

So,
$100 \times 0.\overline{06} \approx 6.06$

Would you like a step-by-step breakdown of another method?

Related Questions:

1. How do you convert repeating decimals into fractions?
2. What is the general formula for converting repeating decimals?
3. How do you multiply fractions and decimals efficiently?
4. How can we approximate repeating decimals without converting them?
5. What are real-life applications of repeating decimals?

Tip: When converting repeating decimals, multiply by a power of 10 that matches the repeating length.