By Chutima S (Dr.เยลลี่)
Published: 27 Aug. 2025
When children start learning elementary mathematics, one of the first things teachers introduce is the [Hindu–arabic numerals] we use to represent numbers. There are 10 digits in total: 0 1 2 3 4 5 6 7 8 and 9. But what do we do if we want to write numbers greater than 9?
In the past, humans used special symbols to represent numbers greater than 9, such as:
[Roman numerals] could be used to express numbers, but as the numbers grew larger, writing and calculation became complicated. For example, adding Roman numerals required substitution and combining symbols, which was not convenient.
Later, the [Hindu–arabic numerals] system that we use today was developed. It works by writing digits next to one another and assigning a different value depending on each position (place)—ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and millions. This system made writing and calculation much more practical. This is the beginning of the concept of [place value], which is a key foundation in elementary mathematics grades 1–6.
The number 12
Written in expanded form: $$ 12 = 10 + 2 $$
The number 365 can be placed in the [place value table] as follows:
| Hundreds | Tens | Ones |
|---|---|---|
| 3 | 6 | 5 |
Written in expanded form: $$ 365 = 300 + 60 + 5 $$
The number 72,051 can be placed in the [place value table] as follows:
| Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|
| 7 | 2 | 0 | 5 | 1 |
Written in expanded form: $$ 72{,}051 = 70{,}000 + 2{,}000 + 0 + 50 + 1 $$
Understanding [place value] is a crucial foundation in elementary mathematics. It connects directly to addition, subtraction, multiplication, division, and more complex problem solving. Children who regularly practice with elementary math exercises will see number relationships more clearly, making classroom learning much easier.
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