Number Bases · Form 4
Number Bases: Key Terms
The key Number Bases terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Number base The number of digits a counting system uses; base ten uses ten digits, base two uses two.
- Place value The value a digit has because of its position; in base five each column is worth five times the one to its right.
- Binary (base two) A number system using only the digits 0 and 1.
- Digit A single symbol used to write a number; base five uses only the digits 0 to 4.
- Base eight (octal) A number system using the digits 0 to 7, where each place is a power of eight.
Term pairs students confuse
- Number base vs digit: the base is how many symbols the system uses and how much each column is worth; a digit is a single symbol inside the number. In 234 (base five), five is the base and 2, 3, 4 are the digits.
- Place value vs face value: the face value is the digit itself, while the place value is the digit multiplied by its column worth. In 234 (base five) the digit 3 has face value 3 but place value 3x5 = 15.
- Binary (base two) vs octal (base eight): both are just number bases, but binary uses only the two digits 0 and 1, while octal uses the eight digits 0 to 7. The larger the base, the fewer digits a given value needs.
- Base ten vs the other bases: base ten is only the everyday default, not a more correct system. The same quantity, 48 in base ten, is 143 in base five and 110000 in base two, all equally valid.
- Carry vs borrow: carrying happens in addition when a column reaches the base and you pass a group up; borrowing happens in subtraction when you take a group of the base value down from the next column. In base five you carry or borrow in groups of five.
How these terms are phrased in real SPM questions
The base almost never appears as the word base in the number itself; it is shown as a small subscript, so 234 (base five) is printed as 234 with a tiny 5 below the line. Instructions come in a few fixed shapes: convert or express asks you to rewrite the value in a stated base, hence signals that you should reuse the answer you just found rather than start over, and state the value of asks for a single figure with its base attached.
A phrase like the number in base five that represents is asking for a conversion in disguise. Reading the subscript first, before the digits, tells you which base you are in and therefore which largest digit is legal, which is why the marks in this topic reward slow, careful reading far more than clever calculation.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What does the small subscript number after a number mean?
It names the base the number is written in. So 234 with a small 5 means 234 in base five, and the digits are read using columns worth 25, 5 and 1 rather than hundreds, tens and units.
Whenever you see a subscript, read it first; it decides every place value and which digits are even allowed in that number.
Is 'binary' the same as 'base two' in an SPM question?
Yes, they are two names for the same thing. Binary means the base-two system, which uses only the digits 0 and 1.
A question may say either word or just show a subscript 2, and all three mean identically the same base. The same holds for octal, which is simply base eight and uses the digits 0 to 7.
When a question says 'hence', what is it telling me to do?
It tells you to build on the answer you just produced rather than starting fresh. In a part that says hence express the value in base two, the value is the base-ten result from the previous part, so you divide that number, not the original one.
Ignoring hence and restarting wastes time and often reintroduces the error you already avoided.