Let's analyze the table provided in the image. The goal is to determine if each number can be written as a fraction and explain the reason based on whether the number is a terminating decimal, a repeating decimal, or neither. Here's the solution:

1. 0.92

   • Can this be written as a fraction? Yes
   • Reason: This is a terminating decimal because it ends after two decimal places.

2. 0.\overline{6} (0.666...)

   • Can this be written as a fraction? Yes
   • Reason: This is a repeating decimal because the digit 6 repeats infinitely. It equals $\frac{2}{3}$.

3. 0.222...

   • Can this be written as a fraction? Yes
   • Reason: This is a repeating decimal because the digit 2 repeats infinitely. It equals $\frac{2}{9}$.

4. 0.257963...

   • Can this be written as a fraction? No
   • Reason: This is a decimal that neither terminates nor repeats, as there is no discernible repeating pattern or end.

Would you like a detailed explanation for any of these, or have further questions? 😊

5 Related Questions:

1. How can repeating decimals always be converted to fractions?
2. Why are some decimals unable to be expressed as fractions?
3. What is the difference between rational and irrational numbers?
4. How does a terminating decimal differ mathematically from a repeating decimal?
5. Can a decimal with no visible pattern ever be written as a fraction?

Tip:

To convert a repeating decimal to a fraction, use algebra: Let $x$ equal the repeating decimal, multiply $x$ to shift the repeating part, then subtract and solve for $x$.