Using the Less Than or Equal Sign
The less than or equal sign combines the strict < with an underbar meaning "or equal". Written a ≤ b, it says a is at most b, so the two may coincide. It is the everyday inequality of maths: interval definitions (0 ≤ t ≤ 1), limits on a variable (n ≤ 100), triangle inequalities and constraints in optimisation all rely on it. The open end always faces the larger value, which is the easy way to remember which way round it goes.
Three shapes, one meaning
Fonts and traditions draw the sign differently. ≤ has one bar beneath the angle, and it is the form used in most English-language books and in Unicode's basic Mathematical Operators block. ⩽ slants the bar parallel to the lower stroke of the angle; British, French and Russian publishers favour it, and LaTeX produces it with \leqslant. ≦ stacks a full equals sign under the angle and is what Japanese and Korean schoolchildren learn. All three mean the same thing, so pick the one that matches the house style and keep it consistent through a document.
Spacing and pairing
As a relation, ≤ takes a space on both sides. A chain such as 1 ≤ x ≤ 10 reads left to right as "x lies between one and ten inclusive". Its partner is the greater than or equal sign; flipping the direction is the only difference, so a ≤ b and b ≥ a are the same statement. The strict version < carries the extra claim that the two sides differ, which is why a ≤ b is often written when a proof needs to allow equality.
In code and spreadsheets
Programming languages type it as two characters, <=, and so do Excel and Google Sheets: =IF(A1<=B1, ...). Pasting ≤ into a formula returns an error. Ligature fonts such as Fira Code draw <= as ≤ on screen, but the underlying text is still ASCII. Regular expressions, URL parameters and command-line tools likewise want the two-character form. The Unicode sign belongs in comments, documentation, user-facing labels and anywhere a human reads rather than a parser.
Typing it
macOS pairs it with the comma key: Option + , gives ≤ and Option + . gives ≥. Windows has no Latin-1 Alt code, but the old DOS code Alt + 243 still functions in many programs, and Word converts 2264 to ≤ after Alt + X. The iPhone keyboard and Gboard both hide it under a long-press of the < key on the symbols page, alongside the « guillemet. In HTML, use ≤.
Everyday writing
Beyond textbooks the sign turns up in dosage instructions ("≤ 4 tablets a day"), event rules ("bags ≤ 40 × 20 cm"), price filters and fitness logs ("≤ 20 g sugar"). It is also a favourite of the arrow symbols crowd, who use ≤ and ≥ as pointed dividers in bios, and it pairs with the not equal sign in maths-flavoured display names.