Express `2/3` as a recurring decimal.

Answer

To express \( \frac{2}{3} \) as a recurring decimal, we can follow these steps:

### Step 1: Set up the division
We need to divide 2 by 3. Since 2 is less than 3, we will start by adding a decimal point and a zero to 2, making it 2.0.

### Step 2: Perform the division
Now, we divide:
- 3 goes into 20 six times (since \( 3 \times 6 = 18 \)).
- Write down 6 after the decimal point.

### Step 3: Subtract and bring down the next zero
- Subtract 18 from 20, which gives us 2.
- Bring down another zero, making it 20 again.

### Step 4: Repeat the division
- Again, 3 goes into 20 six times (since \( 3 \times 6 = 18 \)).
- Write down another 6.

### Step 5: Notice the pattern
- If we continue this process, we will keep getting 20, and thus keep getting 6s. This means the 6 is repeating.

### Step 6: Write the final answer
To indicate that the 6 is repeating, we can write it as:
\[ 0.666\ldots = 0.\overline{6} \]
Thus, \( \frac{2}{3} \) expressed as a recurring decimal is \( 0.\overline{6} \).

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