The number bases chapter shows that our ordinary counting is only one way of writing numbers. You learn to write the same quantity in another base, to convert between bases, and to add and subtract in them.
The chapter sits in SPM Mathematics and is part of the Form 4 Mathematics topics.
How do the four lessons connect?
All four rest on place value, which is why the order matters.
- Converting base ten to another base teaches place value in a new base.
- Converting between non-decimal bases shows how to go from one new base to another.
- Adding and subtracting numbers in different bases uses the column method with the new base.
- Checking place-value errors in base conversions gives you ways to verify every answer.
What does one small number show?
Take 13 in base ten. In base two, the place values are 8, 4, 2 and 1, so 13 = 8 + 4 + 0 + 1, which is written 1101₂.
Add 1 to 1101₂: the units column makes 2, which is 10₂, so it carries once. The result is 1110₂, which is 14. Place value, conversion, addition and checking all appear in this one small number.
Who should start where?
If you are not sure why 1101₂ equals 13, begin at lesson one. If you can convert but the carries go wrong, start at lesson three. If your answers come out with digits that do not exist in the base, such as a 5 in base five, lesson four will help.
Test yourself with the number bases practice set.
When does extra help make sense?
Number base errors are small and systematic, and they often come from one habit, such as carrying ten. A teacher who sees your columns can name the habit quickly.
If that sounds useful, see online one-to-one Mathematics tuition and mention number bases when you enquire.