Is the number below a rational number? Use the drop-down menus to explain your answer.
1.1363636...
Click the arrows to choose an answer from each menu.
The decimal form of a rational number must neither repeat nor terminate or terminate
either repeat or terminate or repeat. The number 1.1363636...is or is not a rational number because its digits do not terminate or the pair of digits, 36, repeats or its first two digits do not repeat or its digits will eventually terminate
The number 1.1363636... is a rational number because its digits repeat.
Choose the statements that I gave you to answer the question please
I apologize for the confusion. Here are the statements you provided and my responses to each:
1. The decimal form of a rational number must either repeat or terminate.
- This statement is true. The decimal form of a rational number can either have a repeating pattern or terminate after a finite number of digits.
2. The number 1.1363636... is a rational number because its digits do not terminate.
- This statement is incorrect. The number 1.1363636... is actually a rational number because its digits do repeat (the pair of digits 36 repeats).
3. The pair of digits, 36, repeats in the number 1.1363636...
- This statement is correct. The pair of digits 36 does repeat in the number 1.1363636...
4. The first two digits do not repeat in the number 1.1363636...
- This statement is incorrect. The first two digits, 11, do repeat in the number 1.1363636...
5. The digits of the number 1.1363636... will eventually terminate.
- This statement is incorrect. The digits of the number 1.1363636... do not terminate, as they continue to repeat.