Question

1/11
What is the decimal expansion of the fraction above?

A. 0.09
B. 0.11
C. 0.09
D. 0.15

Answer 1

To find the decimal expansion of the fraction \( \frac{1}{11} \), you can perform long division.

1. Divide 1 by 11:
- 11 goes into 1 zero times. So we have 0.
- Now consider 1.0 or 10. 11 goes into 10 zero times. So we have 0.0.
- Now consider 100. 11 goes into 100 nine times (since \( 11 \times 9 = 99 \)).
- Subtract 99 from 100, which leaves a remainder of 1.

2. Now, you repeat this process:
- Bring down another 0 to make it 10, and again 11 goes into 10 zero times.
- Bring down 0 again, making it 100.
- Again, 11 goes into 100 nine times, leaving a remainder of 1.

This shows that the decimal repeats.

Thus, the decimal expansion of \( \frac{1}{11} \) is \( 0.090909...\), which can be written as \( 0.\overline{09} \).

Among the provided options:
A. 0.09
B. 0.11
C. 0.09
D. 0.15

The correct answer is **A. 0.09** (though we recognize it's a repeating decimal).