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A fraction consists of two parts, the numerator and the denominator. The numerator, located above the fraction bar, signifies the number of parts we're focusing on. The denominator, below the fraction bar, indicates the total number of equal parts into which the whole is divided.

For example, in the fraction \(\frac{7}{20}\), 7 is the numerator, telling us that there are seven parts in question. The denominator, 20, lets us know that the whole is divided into 20 equal parts. When discussing fractions, recognizing the roles of numerators and denominators is crucial since they outline the proportion of the whole that we are dealing with.

Long division is a method used to divide larger numbers that cannot be easily divided in your head. It's particularly helpful when converting fractions to decimals. The process involves writing the division in a step-by-step manner, bringing down digits from the dividend one by one and subtracting the largest possible multiple of the divisor until the division is complete.

To apply long division for converting the fraction \(\frac{7}{20}\) into a decimal, write 7 (the numerator) inside the division bracket and 20 (the denominator) outside. The division proceeds by determining how many times 20 can go into 7, which is 0 times initially. Then, a decimal point is added to the dividend, and 20 is divided into 70, resulting in 3 with a remainder that leads to further steps until the division is fully resolved.

Decimal representation is the expression of a number in the base-10 numeral system, which consists of a whole number part and a fractional part separated by a decimal point. Converting fractions to decimals is a common practice as it makes comparisons and computations easier.

In the context of the given exercise, achieving the decimal representation of \(\frac{7}{20}\) involves dividing the numerator by the denominator. After executing the long division process, we obtain 0.35, which is the decimal form of the fraction. This decimal signifies the same value as the fraction—it's simply a different way to express the proportion between the numerator and the denominator.