Number Bases · 2.1.1
Numbers in different bases
This standard asks students to understand that a number in any base is built by grouping objects into bundles of that base size, then writing the count of bundles as digits. Students must identify each digit's place value (1, base, base², …) and digit value (digit × place value), and state the total number value.
The official learning standard (2.1.1)
“Represent and explain numbers in various bases in terms of numerals, place values, digit values and number values based on the collection process.”
What it means
This standard asks students to understand that a number in any base is built by grouping objects into bundles of that base size, then writing the count of bundles as digits. Students must identify each digit's place value (1, base, base², …) and digit value (digit × place value), and state the total number value.
How it is examined
This is mostly tested in Paper 1 as a short objective item, for example identifying the place value or digit value of a specified digit in a number written in a stated base, or writing the number value of a bundled-objects diagram. It rarely appears as a standalone Paper 2 question.
Worked example
In the number 324 in base five, state the place value and digit value of the digit 2.
- The number 324 (base five) has place values, from right: 1, 5, 5² = 25.
- The digit 2 is in the 'fives' place (second digit from the right), so its place value is 5.
- Digit value = digit × place value = 2 × 5 = 10.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's the difference between digit value and number value?
Digit value is one digit multiplied by its place value, giving the contribution of that single digit. Number value is the total value of the whole number, the sum of every digit's digit value added together.
Why can't a digit in base 5 be 5 or more?
In base b, only digits 0 to (b − 1) are valid, because reaching b objects in a place means a full bundle has been collected, which is carried over to the next place value instead of being written as a single digit.
How do place values change between bases?
Place values are always powers of the base, read right to left starting at power 0. In base 5 they are 1, 5, 25, 125…; in base 2 they are 1, 2, 4, 8…, the size of each bundle depends entirely on the base.