Express each of the following percentages as a decimal :
`3(1)/(8)%`

Answer

To express `3(1)/(8)%` as a decimal, we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction.
The mixed fraction `3(1)/(8)` can be converted to an improper fraction.

To do this, we multiply the whole number (3) by the denominator (8) and then add the numerator (1):

\[ 3 \times 8 + 1 = 24 + 1 = 25 \]

So, `3(1)/(8)` can be written as:

\[ \frac{25}{8} \]

### Step 2: Convert the percentage to a fraction.
Since we need to express this as a decimal, we convert the percentage to a fraction by dividing by 100:

\[ \frac{25}{8} \% = \frac{25}{8} \div 100 = \frac{25}{8} \times \frac{1}{100} = \frac{25}{800} \]

### Step 3: Simplify the fraction.
Now, we simplify the fraction \(\frac{25}{800}\):

Both the numerator and the denominator can be divided by 25:

\[ \frac{25 \div 25}{800 \div 25} = \frac{1}{32} \]

### Step 4: Convert the fraction to a decimal.
Next, we convert \(\frac{1}{32}\) into a decimal by performing the division:

1. Divide 1 by 32. Since 1 is smaller than 32, we write it as 1.000000.
2. 32 goes into 100 three times (32 x 3 = 96).
3. Subtract 96 from 100 to get 4. Bring down a 0 to make it 40.
4. 32 goes into 40 once (32 x 1 = 32).
5. Subtract 32 from 40 to get 8. Bring down a 0 to make it 80.
6. 32 goes into 80 two times (32 x 2 = 64).
7. Subtract 64 from 80 to get 16. Bring down a 0 to make it 160.
8. 32 goes into 160 five times (32 x 5 = 160).
9. Subtract 160 from 160 to get 0.

So, \(1 \div 32 = 0.03125\).

### Final Answer:
Thus, the decimal representation of `3(1)/(8)%` is:

\[ 0.03125 \]

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