10. what is the same and what is different about the decimal representations 0.\\overline{14} and…
10. what is the same and what is different about the decimal representations 0.\\overline{14} and 0.1\\overline{4}?
Answer
Brief Explanations:
- Same: Both are non - terminating decimals. They have the digits (1) and (4) in the decimal part.
- Different:
- For (0.\overline{14}), the bar is over both (1) and (4), which means the block (14) repeats indefinitely. So (0.\overline{14}=0.141414\cdots).
- For (0.1\overline{4}), the bar is only over (4), which means the digit (4) repeats indefinitely after the (1). So (0.1\overline{4}=0.14444\cdots).
Answer:
- Same: Both are non - terminating decimals with (1) and (4) in the decimal part.
- Different: (0.\overline{14}) has the block (14) repeating ((0.141414\cdots)), while (0.1\overline{4}) has only (4) repeating after (1) ((0.14444\cdots)).