Number Bases · 2.1.4
Solving number base problems
Students apply representation, conversion and calculation skills together to solve multi-step problems involving number bases, for example finding an unknown base or unknown digit from given information, or combining conversion with arithmetic to reach a required answer in a specified base.
The official learning standard (2.1.4)
“Solve problems involving number bases.”
What it means
Students apply representation, conversion and calculation skills together to solve multi-step problems involving number bases, for example finding an unknown base or unknown digit from given information, or combining conversion with arithmetic to reach a required answer in a specified base.
How it is examined
This is examined in Paper 2 as a subjective, multi-mark question, often requiring students to form and solve a simple equation to find an unknown base, or to convert, calculate and convert again across several steps within one real or abstract scenario.
Worked example
Given that 23 in base x is equal to 17 in base 10, find the value of x.
- Express 23 (base x) using place values: 2 × x + 3 × 1 = 2x + 3.
- Since 23 (base x) = 17, form the equation: 2x + 3 = 17.
- Solve: 2x = 14, so x = 7.
- Check: digits 2 and 3 are both less than 7, so base 7 is valid.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What kind of problems combine number bases with other topics?
Number base problems often appear with simple linear equations (finding an unknown base or digit) or combined with conversion and calculation in one question, such as converting two numbers to base 10, adding them, then converting the result to a third base.
How do I know if my answer for an unknown base is valid?
Every digit used in the original number must be smaller than the base you found, if any digit is equal to or larger than your calculated base, that value is impossible and you must recheck your working.
What's a common mistake in multi-step base problems?
A common mistake is mixing up which base a value should be read in halfway through the working, always label each number clearly with its base as a subscript, and convert to base 10 as a common ground before comparing or combining values.