Fractions vs Decimal numbers

Question

I want to know if there is any difference between Fractions and Decimal numbers, are Decimal numbers just Fractions that are written in a different way according to a predefined rule: using "a group of Fractions" that each have a denominator that is smaller 10 times than the one before it.

Answer 1

[edited after reading the comments]

I think I learned as a child that a decimal number is a real number that can be written in the form $a/10^b$ where $a\in\mathbb{Z}$ and $b\in\mathbb{N}$. With this convention there exist rational numbers which are not decimal, e.g $1/3=0.3333...$

But after seeing the comments and having a look at wikipedia it seems this is not the most common definition. So if we consider that

• A decimal number is any real number. The term decimal refers only that we are representing it in base ten.

• A rational number is a real number that can be written in the form $a/b$ where $a,b\in\mathbb{Z}$ and $b\neq0$.

Then any rational number is a decimal number. But there exist decimal number which are not rational, e.g $\sqrt{2}=1.414...$.