Connect with a knowledgeable community and get your questions answered on IDNLearn.com. Discover detailed answers to your questions with our extensive database of expert knowledge.
Sagot :
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].
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].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.