Place value in base ten: why 256 means 256
The decimal system uses ten symbols, 0 to 9. The value of a digit is the digit times the value of its place. Places are counted from the right, starting at zero: the ones place is place 0 and is worth 10⁰ = 1 (ten to the power zero is one), the tens place is place 1 and is worth 10¹ = 10, then 10² = 100 for hundreds and 10³ = 1000 for thousands. Each place is worth ten times the place to its right. Take 4083: four thousands, no hundreds, eight tens and three ones, so 4083 = 4×1000 + 0×100 + 8×10 + 3×1. Written with powers it is 4×10³ + 0×10² + 8×10¹ + 3×10⁰. The 0 is not wasted: it is a placeholder that keeps the 4 in the thousands place. Without it we would have 483, a very different number.
| thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| Place number | 3 | 2 | 1 | 0 |
| Power of ten | 10³ | 10² | 10¹ | 10⁰ |
| Place value | 1000 | 100 | 10 | 1 |
| Digit of 4083 | 4 | 0 | 8 | 3 |
| Digit × value | 4000 | 0 | 80 | 3 |
| Number | Value of the 1 | Value of the 7 |
|---|---|---|
| 5017 | 10 | 7 |
| 5170 | 100 | 70 |
Choose a four-digit number from an invented bus ticket. Draw a table like the one in the lesson with the place names, the powers of ten and the value of each digit, and add the values to check that you get your number back.