Exponentials: An Introduction

The exponentials are distinguished by their notation, which was originally intended to be a simplified way of representing numbers having the form: a single natural number (such as 1,2,3,4,5, ….) multiplied together repeatedly. Perhaps, because counting how many 2’s are multiplied together in the following product 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2• 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 is a rather tedious chore, not to say a time consuming one, a new notation was developed to avoid this dull repetitive presentation which, while correct, was not easy to read. Enter the special number, called an exponential, looking like 2³⁰, instead of 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2• 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 , which is read as the base number 2 multiplied together 30 times.

It is also plausible that, when this notation was introduced, some very knowledgeable people of the time wondered if such numbers would ever become of importance to human kind in general. After all, it would take one person a considerable amount of time to count from 1 up to the value of such a product. For example, if we were to suppose that it takes 1 second to count a single number, then it would take 2³⁰ or 1,073,741,824 seconds to count from 1 to 2³⁰. That translates into about 12,427 ½ days or a tad over 34 years. Well, even if no-one would ever expect any sane person to spend almost one-half of a lifetime counting so as to get a feel for the size of this numerical creature, the majority of people would probably have found this topic quite daunting to study or investigate because of its incessant repetitions of the same thing.

However, mathematicians and scientists often have a way of perceiving and exploring the unusual or the challenging until, one day, the 'extraordinary' has become transformed into ordinary and has become common talk around dinner tables of a future generation. You may well ask: so are you suggesting that numbers like 2³⁰ are commonly discussed today? Actually, yes, that is precisely what I am inferring. In fact, the vernacular word we use today for the exponential number 2³⁰ is 'giga'byte. A gigabyte has 2³⁰ bytes.

Last Updated by SAS October 07, 2026, 16:00:46