Express 0.175 in the form `(p)/(q)`.

Answer

To express the decimal 0.175 in the form \( \frac{p}{q} \), we can follow these steps:

### Step 1: Identify the decimal
The decimal we want to convert is 0.175.

### Step 2: Remove the decimal point
To convert this decimal into a fraction, we can remove the decimal point by multiplying the number by 1000 (since there are three decimal places). Thus, we have:
\[ 0.175 \times 1000 = 175 \]
This means we can express 0.175 as:
\[ \frac{175}{1000} \]

### Step 3: Simplify the fraction
Next, we need to simplify the fraction \( \frac{175}{1000} \). To do this, we find the greatest common divisor (GCD) of 175 and 1000.

- The prime factorization of 175 is \( 5^2 \times 7 \).
- The prime factorization of 1000 is \( 2^3 \times 5^3 \).

The GCD is \( 5^2 = 25 \).

Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{175 \div 25}{1000 \div 25} = \frac{7}{40} \]

### Final Answer
Thus, the decimal 0.175 can be expressed in the form \( \frac{p}{q} \) as:
\[ \frac{7}{40} \]

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