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When we speak about the 'decimal representation' of a number, we are discussing a way to express numbers that uses a base of ten. In our daily lives, we use the decimal system to represent values, making it the most familiar numerical system. The decimal system also allows us to represent fractions, where the digits follow the decimal point, and each place represents a power of ten. For instance, the number 0.875 has an 8 in the tenths place, a 7 in the hundredths place, and a 5 in the thousandths place.

When converting fractions like \(\frac{7}{8}\) to decimals, you essentially translate a given fraction into this familiar base-ten format. This process involves division, which leads us to our next concept: numerators and denominators and their role in converting fractions to decimals.

Understanding the roles of 'numerators and denominators' is pivotal in working with fractions and converting them into decimals. A fraction is composed of two parts: the numerator, which is the top number, and the denominator, which is the bottom number. The numerator represents how many parts we have, while the denominator indicates the total number of equal parts the whole is divided into.

So, for our fraction \(\frac{7}{8}\), the numerator is 7, indicating we have 7 parts, and the denominator is 8, signifying the whole is divided into 8 parts. When we convert this fraction to a decimal, we are essentially calculating how many times the denominator fits into the numerator. This leads us directly into the division process that occurs when we convert any fraction into its decimal form.

The 'division of fractions' is not as daunting as it sounds. It's actually a simple process that can be applied to any fraction to find its decimal equivalent. Essentially, it's the act of dividing the numerator by the denominator. Using our example \(\frac{7}{8}\), to convert this fraction into a decimal, we divide 7 (the numerator) by 8 (the denominator).

This division can be done by hand, with long division, or with a calculator. With long division, you may have to add zeroes to the dividend and bring them down to continue the division until you reach a remainder of zero or until you recognize a repeating decimal. In the case of \(\frac{7}{8}\), when you perform the division, you'll get the decimal 0.875, as seen in step 2 of the solution.