**Expressing 0.63636 in p/q Form**

To express the decimal number 0.63636 in p/q form, where p and q are integers, we need to convert the repeating decimal into a fraction. The notation p/q represents the fraction where p is the numerator and q is the denominator.

**Step 1: Identify the Repeating Part**

The decimal 0.63636 has a repeating part, which is the number 63. To express it as a fraction, we need to determine the length of the repeating part. In this case, the repeating part has a length of 2 digits.

**Step 2: Create an Equation**

Let's assume x = 0.63636 and multiply it by a power of 10 to eliminate the repeating part. Since the repeating part has 2 digits, we can multiply x by 100:

100x = 63.63636

**Step 3: Subtract the Equation**

Now, subtract the original equation from the equation obtained in Step 2 to eliminate the repeating part:

100x - x = 63.63636 - 0.63636

99x = 63

**Step 4: Solve for x**

To solve for x, divide both sides of the equation by 99:

x = 63/99

**Step 5: Simplify the Fraction**

Now, simplify the fraction 63/99 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 9:

63 ÷ 9 / 99 ÷ 9 = 7/11

Hence, the decimal number 0.63636 can be expressed in p/q form as 7/11.

In summary, to express a repeating decimal in p/q form, we follow the steps of identifying the repeating part, creating an equation, subtracting the equation, solving for x, and simplifying the fraction. By following this method, we can convert repeating decimals into fractions.

X=0.63636- eq 1
100x=63.63636(multiply 100 to both sides)-eq2
99x=63(subtract eq 2 from 1)
x=63/99
x=7/11