Question
What is the decimal expansion of the following fraction?
1/18
1/18
Answers
GPT-4o mini
To find the decimal expansion of the fraction \( \frac{1}{18} \), we can perform long division.
When we divide 1 by 18:
1. 18 goes into 1 zero times. So, we write \( 0. \) and consider \( 1.000000 \).
2. 18 goes into 10 zero times (still \( 0. \)).
3. Bring down the next 0, making it 100. 18 goes into 100 five times since \( 18 \times 5 = 90 \).
4. Subtract 90 from 100, which leaves us with 10.
5. Bring down the next 0, making it 100 again. 18 goes into 100 five times again.
6. Subtract again \( 90 \) from \( 100 \) to get \( 10 \).
7. Repeat the process: bring down another 0, we get 100, and so on.
This shows that the decimal goes on as follows:
- \( \frac{1}{18} = 0.055555...\)
The repeating digit 5 can be noted as \( 0.05\overline{5} \).
Thus, the decimal expansion of \( \frac{1}{18} \) is:
\[
0.05555\ldots = 0.05\overline{5}
\]
When we divide 1 by 18:
1. 18 goes into 1 zero times. So, we write \( 0. \) and consider \( 1.000000 \).
2. 18 goes into 10 zero times (still \( 0. \)).
3. Bring down the next 0, making it 100. 18 goes into 100 five times since \( 18 \times 5 = 90 \).
4. Subtract 90 from 100, which leaves us with 10.
5. Bring down the next 0, making it 100 again. 18 goes into 100 five times again.
6. Subtract again \( 90 \) from \( 100 \) to get \( 10 \).
7. Repeat the process: bring down another 0, we get 100, and so on.
This shows that the decimal goes on as follows:
- \( \frac{1}{18} = 0.055555...\)
The repeating digit 5 can be noted as \( 0.05\overline{5} \).
Thus, the decimal expansion of \( \frac{1}{18} \) is:
\[
0.05555\ldots = 0.05\overline{5}
\]