Convert the following decimals into `p//q` form. `(p,q in Z)`
35.2

Answer

To convert the decimal 35.2 into the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Decimal**: Start with the decimal number you want to convert.
\[ 35.2 \]

2. **Eliminate the Decimal Point**: To convert the decimal to a fraction, we can express it as a fraction with a numerator and a denominator. First, we can write:
\[ 35.2 = \frac{352}{10} \]
Here, we moved the decimal point one place to the right, which means we multiply by 10.

3. **Simplify the Fraction**: Now, we need to simplify the fraction \( \frac{352}{10} \). We can find the greatest common divisor (GCD) of 352 and 10 to simplify it.
- The GCD of 352 and 10 is 2.
- Now, divide both the numerator and the denominator by their GCD:
\[ \frac{352 \div 2}{10 \div 2} = \frac{176}{5} \]

4. **Final Result**: The fraction \( \frac{176}{5} \) is in the form \( \frac{p}{q} \), where \( p = 176 \) and \( q = 5 \).

### Final Answer:
\[ 35.2 = \frac{176}{5} \]