Difference Between Numeric and Decimal

Numeric vs Decimal

In mathematics, both the words numeric and decimal refer to numbers which are mathematical objects that are being used to represent values. Though they refer, basically, to the same entity, numerics define a broader class, of which decimals are a subclass. The key idea that can be used to differentiate between these two words is the existence of more than one representation for any given number.

What is Numeric?

The word numeric, which is synonymous with the word number, refers to any number in mathematics regardless of its representation. For example, both the numbers 94.67 and (1011.001)₂ are numerics even though the former was in base 10 and the latter was in base 2. Even the number MMXI (which is in roman numerals and equivalent to 2011 in Hindu-Arabic numerals) is a numeric.

Mathematical representation of a number changes according to the base as well as the type of numerals used in writing the number. Regardless of the base and regardless of the type of the numerals, every number is a numeric.

What is Decimal?

Decimals also refer to numbers, but decimals are not just numbers, they are the numbers represented in base 10. For example, 94.67 is a decimal as it is represented in base 10. Yet, (1011.001)₂ is not a decimal as it is in base 2. Simply, it can be stated that a decimal is a numeric represented in base 10. This also confirms that all decimals belong to the broader class of numerics.

In general, a decimal will take the form m₁10ⁿ+m₂10^n-1+…+ m_n+110⁰+m_n+210^-1+…+m_n+p+110^-p, where n, p are all positive integers, m_i’s are from 0, 1, 2 … 9 and m₁, m_n+p+1 are non-zero. Since the representation of a number in base 10 is unique, there cannot be two representations for the same decimal. In other words, if two combinations of digits refer to the same decimal, those two combinations should be equal.