Number Bases · 2.1.2
Converting between number bases
Students learn several methods to change a number from one base into another: repeated division by the target base (from base 10), expanding by place value (into base 10), and using base 10 as an intermediate step when converting directly between two non-decimal bases.
The official learning standard (2.1.2)
“Convert numbers from one base to another using various methods.”
What it means
Students learn several methods to change a number from one base into another: repeated division by the target base (from base 10), expanding by place value (into base 10), and using base 10 as an intermediate step when converting directly between two non-decimal bases.
How it is examined
Paper 1 usually includes a short item converting a single number between two bases. Paper 2 may combine conversion with a follow-up step, such as performing a calculation on the converted number or using it within a larger number-base problem.
Worked example
Convert 46 (base 10) to base 2.
- Divide 46 by 2: 46 ÷ 2 = 23 remainder 0.
- Divide 23 by 2: 23 ÷ 2 = 11 remainder 1.
- Divide 11 by 2: 11 ÷ 2 = 5 remainder 1.
- Divide 5 by 2: 5 ÷ 2 = 2 remainder 1.
- Divide 2 by 2: 2 ÷ 2 = 1 remainder 0.
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1.
- Read the remainders from bottom to top: 101110.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How do I convert directly between two non-decimal bases, like base 3 to base 5?
There is no direct shortcut, first expand the base 3 number using place values to find its base 10 value, then use repeated division by 5 on that base 10 value to get the base 5 digits.
Why do I read the remainders from bottom to top?
Each division finds one digit starting from the smallest place value (units) and working towards the largest, so the first remainder found is the last digit of the answer, and the last remainder found is the first digit.
What's a quick way to check my conversion is correct?
Convert your final answer back to base 10 by expanding each digit × its place value and summing. If the total matches the original base 10 number, your conversion is correct.