Formulas and rules
Every key math formula and rule, organised by topic and school level, with examples and study tips.
Numbers 7
Place value
digit x 10^n
Each digit is worth ten times more as you move one place to the left.
The number line
Numbers are ordered on a line: moving right adds, moving left subtracts.
Negative numbers
-a + b = b - a
Numbers below zero are negative. Adding a negative moves left, subtracting a negative moves right.
Order of operations (BIDMAS)
Brackets, Indices, Division/Multiplication, Addition/Subtraction
Work through brackets first, then powers, then multiplication and division left to right, then addition and subtraction.
Rounding
Look at the digit after the place you round to: 5 or more rounds up, less than 5 rounds down.
Powers and roots
a^n = a x a x ... (n times) ; sqrt(a^2) = a
A power is repeated multiplication. A square root undoes a square.
Scientific notation
a x 10^n with 1 <= a < 10
Write very large or very small numbers as a number between 1 and 10 times a power of ten.