Express 0.875 in the form `(p)/(q)`.

Answer

To express 0.875 in the form of \( \frac{p}{q} \), we can follow these steps:

### Step-by-Step Solution:

1. **Let \( x = 0.875 \)**:
- We start by defining our variable \( x \) to represent the decimal number we want to convert.

**Hint**: Define the decimal as a variable for easier manipulation.

2. **Multiply by 1000 to eliminate the decimal**:
- Since there are three digits after the decimal point, we multiply both sides of the equation by 1000:
\[ 1000x = 875 \]

**Hint**: Multiplying by a power of 10 helps to shift the decimal point to the right.

3. **Rearranging the equation**:
- Now, we can express \( x \) in terms of a fraction:
\[ x = \frac{875}{1000} \]

**Hint**: This step involves rewriting the equation to isolate \( x \).

4. **Simplifying the fraction**:
- Next, we need to simplify \( \frac{875}{1000} \). We can find the greatest common divisor (GCD) of 875 and 1000. The GCD is 125.
- Now, divide both the numerator and the denominator by 125:
\[ \frac{875 \div 125}{1000 \div 125} = \frac{7}{8} \]

**Hint**: Simplifying fractions involves dividing both the numerator and denominator by their GCD.

5. **Final expression**:
- Thus, we have expressed 0.875 in the form \( \frac{p}{q} \):
\[ x = \frac{7}{8} \]

**Hint**: Ensure that the denominator \( q \) is not zero, which is a requirement for a valid fraction.

### Conclusion:
- Therefore, \( 0.875 \) can be expressed as \( \frac{7}{8} \), where \( p = 7 \) and \( q = 8 \).