To express 20.4545 as a fraction, we need to break it down:

Step 1: Separate the whole number and the decimal part.

• Whole number = $20$
• Decimal part = $0.4545$

Step 2: Convert the repeating decimal $0.4545...$ into a fraction.

Let $x = 0.4545...$

Multiply both sides by 100 (since two digits repeat): $100x = 45.4545...$

Now, subtract the original equation from this one: $100x - x = 45.4545... - 0.4545...$ $99x = 45$

Solve for $x$: $x = \frac{45}{99} = \frac{5}{11}$

Step 3: Add the whole number part back.

Now that we know $0.4545 = \frac{5}{11}$, we add it to the whole number $20$: $20 + \frac{5}{11} = \frac{20 \times 11}{11} + \frac{5}{11} = \frac{220 + 5}{11} = \frac{225}{11}$

So, $20.4545...$ as a fraction is $\frac{225}{11}$.

Would you like more details, or do you have any questions?

Related questions:

1. How can repeating decimals be converted into fractions?
2. How do you simplify fractions?
3. What is the difference between repeating and non-repeating decimals?
4. Can any repeating decimal be written as a fraction?
5. How do you add fractions with different denominators?

Tip:

Always look for patterns in repeating decimals when converting them into fractions.