The problem in the image asks to show that the number 0.747474... (a repeating decimal) is rational by writing it as a ratio of two integers.

Solution:

To express $0.747474\ldots$ (repeating) as a fraction:

1. Let $x = 0.74747474\ldots$.

2. Multiply both sides by 100 to shift the decimal two places to the right: $100x = 74.74747474\ldots$

3. Now subtract the original equation $x = 0.747474\ldots$ from this new equation: $100x - x = 74.747474\ldots - 0.747474\ldots$ This simplifies to: $99x = 74$

4. Solve for $x$: $x = \frac{74}{99}$

Thus, $0.747474\ldots = \frac{74}{99}$, showing that it is a rational number.

This matches the answer shown in the image, which is $\frac{74}{99}$.

Do you have any questions or would you like more details on this solution?

Here are 5 related questions for further exploration:

1. How can you convert a non-repeating decimal to a fraction?
2. What is the general method for converting repeating decimals into fractions?
3. Can every repeating decimal be expressed as a fraction?
4. What is the difference between a rational and an irrational number?
5. How can you simplify fractions derived from repeating decimals?

Tip: When converting repeating decimals to fractions, always try multiplying by powers of 10 to eliminate the repeating part during subtraction.