Number Bases
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.
| English | Place value |
|---|---|
| Bahasa Melayu | Nilai tempat |
| 中文 | 位值 |
How it is used
In 342 base five, the digit 3 sits in the 5² column, so its place value is 3×25 = 75 in base ten; the whole number is 75 + 20 + 2 = 97₁₀.
Where it shows up in SPM
Place value is the tool for every conversion in the Number Bases chapter (Form 5). Paper 1 may ask for the value of an underlined digit; Paper 2 uses it in the expanded working when you convert a number in base two, five or eight into base ten.
Don't confuse it with
Open the chapter: Number Bases →
Frequently asked questions
What are the column values in base eight?
Reading from the right, the columns are 8⁰=1, 8¹=8, 8²=64, 8³=512, and so on. So in 57₈ the 5 is worth 5×8 = 40 and the 7 is worth 7, giving 47 in base ten.
Why does the same digit mean different amounts?
Because its worth depends on its column. In 11₂ the left 1 sits in the 2¹ column worth 2 and the right 1 is worth 1, so 11₂ = 3.
Position, not the symbol alone, decides the value.