ℚ
ℚ Rational Numbers Symbol
ℚ is the set of rational numbers — every number expressible as a fraction a/b with integers a and b, and b not zero. The Q is for quotient.
Also known as: rational numbers symbol, set of rational numbers, double struck q, fractions set symbol.
Codes
| Symbol | ℚ | |
| Unicode | U+211A | |
| HTML entity (named) | ℚ | |
| HTML entity (decimal) | ℚ | |
| HTML entity (hex) | ℚ | |
| CSS | \211A | |
| LaTeX | \mathbb{Q} | |
| Windows Alt code | Alt + 8474 |
How to type ℚ (Rational Numbers Symbol)
Windows211A, Alt + X
In Word, type 211A then press Alt + X. Elsewhere, copy ℚ above or use Character Map (search “double-struck”).
Mac
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “double-struck capital Q”, or copy ℚ above.
Microsoft Word211A, Alt + X
Type 211A, then press Alt + X to convert it to ℚ.
Google Docs
Insert → Equation, then type \Q or \mathbb followed by Q.
LaTeX\mathbb{Q}
Use \mathbb{Q} in math mode (requires amssymb or amsfonts).
Usage
- ℚ is every number you can write as a fraction of integers: 1/2, −7, 0.25 (= 1/4) and 0.333… (= 1/3) are all rational.
- The chain is ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ. What ℚ leaves out are the irrationals — √2, π and e cannot be written as a ratio of integers, and they are what fill the gaps to make up ℝ.
- A number is rational exactly when its decimal expansion terminates or eventually repeats. That is a clean test: 0.125 and 0.142857142857… are rational; π's digits do neither.
- Q is for quotient — the Italian quoziente, via Peano. It is not for “rational”, which is why the letter looks unrelated to the name.