Which is largest in ` 16(2)/(3) % , (2) /(15)` and 0.12 ?

Answer

To determine which of the three values \( 16\frac{2}{3}\% \), \( \frac{2}{15} \), and \( 0.12 \) is the largest, we will convert each of them into decimal form for easy comparison.

### Step 1: Convert \( 16\frac{2}{3}\% \) to Decimal
1. First, convert the mixed fraction \( 16\frac{2}{3} \) into an improper fraction:
\[ 16\frac{2}{3} = \frac{16 \times 3 + 2}{3} = \frac{48 + 2}{3} = \frac{50}{3} \]
2. Now, convert the percentage to decimal by dividing by 100:
\[ \frac{50}{3} \% = \frac{50}{3} \times \frac{1}{100} = \frac{50}{300} = \frac{1}{6} \]
3. Convert \( \frac{1}{6} \) to decimal:
\[ \frac{1}{6} \approx 0.1667 \quad (\text{approximately, as } 0.1666\ldots) \]

### Step 2: Convert \( \frac{2}{15} \) to Decimal
1. Divide \( 2 \) by \( 15 \):
\[ 2 \div 15 = 0.1333\ldots \quad (\text{approximately } 0.1333) \]

### Step 3: Identify the Decimal for \( 0.12 \)
- The third number is already in decimal form:
\[ 0.12 \]

### Step 4: Compare the Values
Now we have the decimal equivalents:
- \( 16\frac{2}{3}\% \approx 0.1667 \)
- \( \frac{2}{15} \approx 0.1333 \)
- \( 0.12 \)

### Step 5: Determine the Largest Value
Comparing the three values:
- \( 0.1667 > 0.1333 > 0.12 \)

Thus, the largest number is:
\[ \boxed{16\frac{2}{3}\%} \]