Number Bases, terms

Start with place value and number base itself, every other idea depends on understanding that a digit's value changes with its position and the base used. Once that is solid, binary (base two) and octal (base eight) become straightforward, since they follow the exact same place-value pattern, just with different digit limits.

Students often forget that a digit's value depends on both its place and the base, so 12 in base three is not the same size as 12 in base ten. Another common slip is writing a digit equal to or larger than the base itself, in base eight, digits only go up to 7.

Questions usually say "convert" or "express in base …", asking you to change a number from one base to another, or to add or subtract numbers already written in a given base. Some also test place value directly, asking you to state the value of a particular digit within a number.