`8.(1/3)%` expressed as a fraction is

Options

A. `25/3`
B. `3/25`
C. `1/12`
D. `1/4`

Answer

To express \( 8 \frac{1}{3} \% \) as a fraction, follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, convert \( 8 \frac{1}{3} \) into an improper fraction.

To do this:
- Multiply the whole number (8) by the denominator (3):
\( 8 \times 3 = 24 \)
- Add the numerator (1) to this result:
\( 24 + 1 = 25 \)

So, \( 8 \frac{1}{3} \) can be expressed as:
\[ \frac{25}{3} \]

### Step 2: Convert the percentage to a fraction
Next, we need to express \( 8 \frac{1}{3} \% \) as a fraction. Recall that percent means "per hundred," so we write:
\[ 8 \frac{1}{3} \% = \frac{25}{3} \times \frac{1}{100} \]

This can be written as:
\[ \frac{25}{3 \times 100} = \frac{25}{300} \]

### Step 3: Simplify the fraction
Now, we simplify \( \frac{25}{300} \). To do this, we find the greatest common divisor (GCD) of the numerator and denominator.

The GCD of 25 and 300 is 25. Now divide both the numerator and denominator by 25:
\[ \frac{25 \div 25}{300 \div 25} = \frac{1}{12} \]

### Final Answer
Thus, \( 8 \frac{1}{3} \% \) expressed as a fraction is:
\[ \frac{1}{12} \]

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