To find the decimal representation of [tex]\(\frac{5}{11}\)[/tex], we need to perform the division of 5 by 11.
When we divide 5 by 11, we start by inserting a decimal point and adding zeros.
1. [tex]\(5 \div 11 = 0\)[/tex]
- Since 5 is less than 11, the whole number part is 0 and we proceed to the decimal part.
2. [tex]\(50 \div 11 \approx 4\)[/tex]
- 11 goes into 50 four times (because [tex]\(11 \times 4 = 44\)[/tex]), leaving a remainder of [tex]\(50 - 44 = 6\)[/tex].
3. [tex]\(60 \div 11 \approx 5\)[/tex]
- 11 goes into 60 five times (because [tex]\(11 \times 5 = 55\)[/tex]), leaving a remainder of [tex]\(60 - 55 = 5\)[/tex].
4. [tex]\(50 \div 11\)[/tex]
- As earlier, this gives us another 4, leading us back to step 2.
Notice the repetition here: the sequence '45' begins to repeat indefinitely.
Thus, the decimal representation of [tex]\(\frac{5}{11}\)[/tex] is [tex]\(0.\overline{45}\)[/tex].
Comparing this with the options given:
- [tex]\(0 . \overline{45}\)[/tex]
- [tex]\(2 . \overline{2}\)[/tex]
- 2.2
- [tex]\(0.0 \overline{45}\)[/tex]
The correct representation is [tex]\(0 . \overline{45}\)[/tex].
So, the decimal representation of [tex]\(\frac{5}{11}\)[/tex] is:
[tex]\[ 0 . \overline{45} \][/tex]
