To find the decimal representation of the fraction [tex]\(\frac{5}{11}\)[/tex], follow these steps:
1. Set up the division:
- We need to divide 5 by 11.
2. Perform the division:
- When 5 is divided by 11, we find that 11 does not divide into 5. Therefore, we append a decimal point and add a zero to 5, making it 50.
- 11 goes into 50 four times (11 4 = 44). So, we write 4 and our remainder is 6 (50 - 44 = 6).
- Now, we bring down another zero, making it 60.
- 11 goes into 60 five times (11 5 = 55). So, we write 5 and our remainder is 5 (60 - 55 = 5).
- Again, we bring down another zero, making it 50.
3. Repeat the process:
- Notice that we are now back to the same situation we started with (dividing 50 by 11). Thus, the decimal digits will start repeating.
4. Identify the repeating pattern:
- The sequence "45" repeats indefinitely.
So, the decimal representation of [tex]\(\frac{5}{11}\)[/tex] is [tex]\(0.45454545454545453\)[/tex] which can be expressed as [tex]\(0.\overline{45}\)[/tex], indicating that "45" is the repeating sequence.
Among the given options:
- 2.2 is not correct.
- [tex]\(0.\overline{45}\)[/tex] is correct.
- 0.045 is not correct.
- [tex]\(2.\overline{2}\)[/tex] is not correct.
Therefore, the correct answer is [tex]\(0.\overline{45}\)[/tex].
