Which of the following will have the MAXIMUM number of 6's when written in decimal form?

Options

A. `(666)/(1000)`
B. `(3)/(6)`
C. `(3)/(5)`
D. `(2)/(3)`

Answer

To determine which of the given options has the maximum number of 6's when written in decimal form, we will evaluate each option step by step.

### Step 1: Evaluate each option

1. **Option 1: \( \frac{666}{1000} \)**
- Calculation:
\[ \frac{666}{1000} = 0.666 \]
- Number of 6's: 3 (from 0.666)

2. **Option 2: \( \frac{3}{6} \)**
- Calculation:
\[ \frac{3}{6} = \frac{1}{2} = 0.5 \]
- Number of 6's: 0 (from 0.5)

3. **Option 3: \( \frac{3}{5} \)**
- Calculation:
\[ \frac{3}{5} = 0.6 \]
- Number of 6's: 1 (from 0.6)

4. **Option 4: \( \frac{2}{3} \)**
- Calculation:
\[ \frac{2}{3} = 0.66666... \text{ (non-terminating)} \]
- Number of 6's: Infinite (as it continues with 6's)

### Step 2: Compare the results
- Option 1 has 3 sixes.
- Option 2 has 0 sixes.
- Option 3 has 1 six.
- Option 4 has an infinite number of sixes.

### Conclusion
The option with the maximum number of 6's when written in decimal form is **Option 4: \( \frac{2}{3} \)**.

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