It looks like you have uploaded a screenshot of a math question asking to determine whether certain numbers can be written as fractions, along with reasons based on the type of decimal (terminating, repeating, or non-terminating/non-repeating).

Here are some clarifications:

1. For 0.898989...:

   • This is a repeating decimal because "89" repeats indefinitely.
   • Any repeating decimal can be written as a fraction. So, the correct response should be:
     • Yes for "Can this be written as a fraction?".
     • This is a repeating decimal for the reason.

2. For 0.92847...:

   • If the digits continue without repeating or terminating, this would be a non-terminating and non-repeating decimal.
   • Non-repeating decimals cannot be written as fractions (they are considered irrational numbers).
   • Therefore, the correct response should be:
     • No for "Can this be written as a fraction?".
     • This is a decimal that neither terminates nor repeats.

3. For 0.555:

   • This is a terminating decimal since it ends after three decimal places.
   • Terminating decimals can always be written as fractions (0.555 = 555/1000).
   • Therefore, the correct response should be:
     • Yes for "Can this be written as a fraction?".
     • This is a terminating decimal for the reason.

Would you like further details on how to convert these decimals into fractions or discuss any of the concepts?

Here are 5 related questions to deepen your understanding:

1. How can you convert a repeating decimal like 0.898989... into a fraction step by step?
2. What is the difference between a repeating decimal and a terminating decimal?
3. Why are non-terminating, non-repeating decimals considered irrational numbers?
4. How can you identify if a decimal is repeating without writing out many digits?
5. Can all repeating decimals be expressed as fractions, and how is this proven?

Tip: Remember that any decimal that repeats or terminates can always be written as a fraction, but non-repeating, non-terminating decimals cannot!