Find the value of :
`166(2)/(3)%` of 3 metres.

Answer

To solve the question, "Find the value of 166(2/3)% of 3 metres," we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
First, we need to convert the mixed number 166(2/3) into an improper fraction.

- To do this, multiply the whole number (166) by the denominator (3) and then add the numerator (2):
\[ 166 \times 3 + 2 = 498 + 2 = 500 \]
- Therefore, we can express 166(2/3) as:
\[ \frac{500}{3} \]

### Step 2: Convert the percentage to a fraction
Next, we need to convert the percentage to a fraction. Since we are dealing with a percentage, we can express it as:
\[ \frac{500}{3} \% = \frac{500}{3} \times \frac{1}{100} \]

### Step 3: Multiply the percentage fraction by 3 metres
Now we will find 166(2/3)% of 3 metres by multiplying the fraction we found by 3:
\[ \frac{500}{3} \times \frac{1}{100} \times 3 \]

### Step 4: Simplify the expression
Now we simplify the expression:
- The 3 in the numerator and denominator cancels out:
\[ \frac{500}{3} \times \frac{1}{100} \times 3 = \frac{500}{100} \]
- Now simplify \(\frac{500}{100}\):
\[ \frac{500}{100} = 5 \]

### Final Answer
Thus, the value of 166(2/3)% of 3 metres is:
\[ \text{5 metres} \]

---