The problem in the image asks to convert the fraction $\frac{4}{7}$ to a decimal and choose the correct answer, with the options provided.

Step 1: Convert the fraction to a decimal

To convert $\frac{4}{7}$ to a decimal, divide 4 by 7:

$\frac{4}{7} \approx 0.5714285714285714$

This decimal is repeating with a pattern of "571428".

Step 2: Rounding the decimal

Since the question specifies to choose the one with the correct digits after rounding, we need to round the decimal accordingly:

• 0.571 when rounded to three decimal places.
• 0.5714 when rounded to four decimal places.

Conclusion

The correct answer that corresponds to the repeating decimal $\frac{4}{7}$ and matches the rounding would be 0.571 when rounded to three decimal places.

Answer:

• Option C: 0.571 is the correct answer.

Would you like any further details or explanations?

Here are five related questions to expand your understanding:

1. How do you convert a repeating decimal back into a fraction?
2. What is the decimal representation of the fraction $\frac{1}{3}$?
3. Why do some fractions have repeating decimals, while others do not?
4. How would you express $0.333\ldots$ (repeating) as a fraction?
5. How do you determine the number of digits in the repeating sequence of a fraction?

Tip: To identify whether a fraction will have a repeating or terminating decimal, check if the denominator has only the prime factors 2 and 5. If it does, the decimal will terminate; otherwise, it will repeat.