# Fractions vs Decimal numbers

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.

• It depends on what definitions you are using for those two terms. Sometimes, people use "fraction" to mean any real number between zero and one; sometimes, people use "fraction" to mean something of the form $a/b$ with $a$ and $b$ integers, $b$ positive. Gilles and I use different definitions of "decimal number". What definitions do you have in mind? Commented Feb 3, 2015 at 12:02
• I say, WHAT DEFINITIONS DO YOU HAVE IN MIND? Commented Feb 4, 2015 at 12:12
• Decimals are simply fractions where the divisor is some power of 10. For example $\frac{1}{4}=\frac{25}{100}$ usually written a $0.25$ and common knowledge lets us know that it is $25$ divided by $100$. If you type a decimal into a cell in Excel and then go to format cells, number and then select fraction 2-digit, you will see, for example. that $0.351\approx \frac{33}{94}$ Commented Oct 13, 2020 at 4:28

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 $1/3=0.3333...$
• 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 $\sqrt{2}=1.414...$.
• Maybe we are using different definitions of "decimal number", but I would say $0.333\dots$ is a decimal number; I'd also say $\sqrt2=1.41421356\dots$ is a decimal number that can't be written as a fraction. Commented Feb 3, 2015 at 11:59