The image provided contains a table with decimals, asking whether each can be written as a fraction, along with the reason for the answer.

Here's the solution:

1. 0.646464…:

   • Can this be written as a fraction?: Yes
   • Reason: This is a repeating decimal. The decimal part "64" repeats infinitely (0.646464…), so it is a repeating decimal and can be expressed as a fraction.

2. 0.63758…:

   • Can this be written as a fraction?: No
   • Reason: This is a decimal that neither terminates nor repeats. The decimal continues without any clear pattern, so it cannot be written as a fraction.

3. 0.222:

   • Can this be written as a fraction?: Yes
   • Reason: This is a terminating decimal. It stops at 0.222, meaning it can be written as a fraction.

4. 0.46 (with the bar above 6):

   • Can this be written as a fraction?: Yes
   • Reason: This is a repeating decimal. The "6" repeats infinitely (0.4666…), so it is a repeating decimal and can be written as a fraction.

Let me know if you'd like details on how to convert any of these decimals to fractions!

5 Related Questions:

1. How do you convert a repeating decimal like 0.6464... into a fraction?
2. Why can't non-repeating and non-terminating decimals be written as fractions?
3. Can all terminating decimals be written as fractions? How?
4. How do we determine whether a decimal is repeating or terminating?
5. What is the method to convert a repeating decimal like 0.46̅ into a fraction?

Tip:

A repeating decimal can always be written as a fraction, whereas a non-repeating, non-terminating decimal cannot.