Final answer:
Options a (0.78) and c (0.78) are equivalent because they both have the same recurring decimal pattern '78'. The correct options are a,c.
Step-by-step explanation:
To determine which two of the recurring decimals are equivalent, we need to look at the pattern of the digits that repeat. In the list provided, we have:
- a. 0.78
- b. 0.785
- c. 0.78
- d. 0.787
The recurring part of a decimal is indicated by placing a bar over the digits that repeat indefinitely. In this context, we assume that '0.78' in option a and c means '0.787878...' and '0.787' in option d means '0.787787...'. It is then clear that option a and option c are equivalent because they have the same recurring part '78'. Options b and d have different digits within their recurring parts, making them different from a and c, as well as from each other.
Therefore, the correct options are: