Which is greatest among `33 1/2%, 4/15` and 0.35?

Options

A. 0.35
B. Cannot be compared
C. `33 1/2%`
D. `4/15`

Answer

To determine which is the greatest among \(33 \frac{1}{2}\%\), \(\frac{4}{15}\), and \(0.35\), we will convert each value into a decimal format for easy comparison.

### Step 1: Convert \(33 \frac{1}{2}\%\) to a decimal
To convert \(33 \frac{1}{2}\%\) to a decimal:
1. Convert the mixed number to an improper fraction:
\[ 33 \frac{1}{2} = \frac{67}{2} \]
2. Convert the percentage to a decimal by dividing by 100:
\[ \frac{67}{2} \div 100 = \frac{67}{200} = 0.335 \]

### Step 2: Convert \(\frac{4}{15}\) to a decimal
To convert \(\frac{4}{15}\) to a decimal:
1. Divide 4 by 15:
\[ 4 \div 15 \approx 0.2667 \]

### Step 3: Compare the decimals
Now we have the following values in decimal form:
- \(33 \frac{1}{2}\% = 0.335\)
- \(\frac{4}{15} \approx 0.2667\)
- \(0.35\)

### Step 4: Identify the greatest value
Now we compare the three decimal values:
- \(0.335\)
- \(0.2667\)
- \(0.35\)

Clearly, \(0.35\) is greater than both \(0.335\) and \(0.2667\).

### Conclusion
Thus, the greatest among \(33 \frac{1}{2}\%\), \(\frac{4}{15}\), and \(0.35\) is:
\[ \boxed{0.35} \]