Question

Which decimal is the equivalent of 6/11
?
A
0.183‾0.18\overline{3}0.18
3

B
0.183‾0.1\overline{83}0.1
83

C
0.54‾0.5\overline{4}0.5
4

D
0.54‾0.\overline{54}0.
54

Answer 1

To find the decimal equivalent of \( \frac{6}{11} \), we can perform long division of 6 by 11.

1. 11 goes into 60 (the first two digits) 5 times, since \( 11 \times 5 = 55 \).
- Write 5 as the first decimal place.
- Subtract: \( 60 - 55 = 5 \).

2. Bring down a 0 to make it 50. 11 goes into 50 four times, since \( 11 \times 4 = 44 \).
- Write 4 as the next decimal place.
- Subtract: \( 50 - 44 = 6 \).

3. Bring down another 0 to make it 60 again. Now we are back to where we started.

This shows that the decimal repeats every two digits: \( 0.545454... \), which can be written as \( 0.\overline{54} \).

Thus, the decimal equivalent of \( \frac{6}{11} \) is:

**D: \( 0.\overline{54} \)**.