Inspiring Young Minds: The Dennis Decimal Theory The Dennis Decimal Theory By Dennis Amoah II

Math, Poems, Stories

Chapter 1: The Meaning of Useful and Useless Numbers

In this theory, I divide numbers into two categories: useful numbers and useless numbers.

A useful number is a number that:

- Divides into 1 and gives a clean, terminating decimal.

- Is easy to use in division and gives simple answers.

Examples:

- 1 ÷ 2 = 0.5

- 1 ÷ 4 = 0.25

- 1 ÷ 5 = 0.2

- 1 ÷ 8 = 0.125

- 1 ÷ 10 = 0.1

- 1 ÷ 16 = 0.0625

- 1 ÷ 20 = 0.05

All of these numbers divide into 1 with neat, short decimals. That is why they are useful.

A useless number is a number that:

- Does not divide into 1 with a clean decimal.

- Gives an endless or repeating decimal that is hard to work with.

Examples:

- 1 ÷ 3 = 0.333...

- 1 ÷ 6 = 0.1666...

- 1 ÷ 7 = 0.142857...

- 1 ÷ 9 = 0.111...

These are useless numbers because they make math messier when dividing into 1.

Chapter 2: Semi-Useful Numbers

Some numbers are not completely useless or useful. I call these semi-useful or semi-useless.

For example:

- 12 is divisible by 4 (which is useful), but also by 3 (which is useless).

- 1 ÷ 12 = 0.0833... (a repeating decimal)

So 12 is semi-useful because it connects to useful numbers like 4 but doesn't give a clean decimal into 1.

Chapter 3: Irrational Numbers and Their Usefulness

An irrational number is any real number that:

- Cannot be written as a fraction

- Never ends and never repeats

Examples:

- π (pi) ≈ 3.14159...

- √2 ≈ 1.4142135...

- e ≈ 2.71828...

These numbers go on forever and never settle into a pattern.

So are irrational numbers useless?

My answer: No, they are semi-useful.

- π (pi) is needed for working with circles.

- √2 is used in geometry and physics.

- 1 ÷ π gives a never-ending decimal, but it is still useful in real life.

So just like useless numbers, irrational numbers are:

"semi-useless and semi-useful."

They are not clean, but they are powerful.

Chapter 4: The Law of Decimal Usefulness

"Due to their ability to go into 1, useful numbers can go into any number."

This is my first law. It means that if a number divides 1 cleanly, it will divide other numbers easily too.

- 37 ÷ 4 = 9.25

- 37 ÷ 5 = 7.4

- 37 ÷ 8 = 4.625

- 37 ÷ 10 = 3.7

All of these are clean because the denominator is useful.

Chapter 5: The Infinity Trap

Yes, you can round a number like 1⁄3 to 0.33, but that doesn't make it truly clean.

Rounding only hides the truth. It cuts off the rest of the decimal and pretends it's over. But in reality:

- 1⁄3 is really 0.33333... going on forever.

- 0.33 is not the same as 1⁄3 — it’s just close.

Some decimals get close… but never arrive:

- 0.333… × 3 = 0.99999…

- That’s really close to 1 — but not exactly 1.

This is a common trait of useless and semi-useful numbers:

- They chase the answer.

- They get closer and closer.

- But they never land perfectly.

"The human mind works such that the more 3s you add at the end, the closer it feels to 1. But it will never truly be 1."

So:

"Some numbers trick us into thinking they’re clean — but true cleanliness can only come from exact division."

This is called the Infinity Trap — a new idea in the Dennis Decimal Theory.

Chapter 6: Open Questions

These are the questions I'm still thinking about:

- Can a number be completely useless?

- Is there a number more useless than π?

- Can we find patterns in which numbers are useful or semi-useful?

Final Thought

Not all numbers have to be clean to be powerful. Some are messy, some are endless, and some are perfect. But every number, in its own way, tells a story.

"Even the most useless number may be useful to someone who understands it."