An exponent counts the tens. Each ten moves every digit one place, and the place sets the value.
1What the Exponent Counts
Power
Tens multiplied
Value
101
10
10
102
10 × 10
100
103
10 × 10 × 10
1,000
104
10 × 10 × 10 × 10
10,000
The exponent counts tens multiplied, not the answer. Three tens make 1,000, never 30. The zeros match the exponent.
2Multiply: Digits Move Left
2.6 × 102 = 260
Two tens make every digit worth a hundred times more, so each moves two places left. A zero fills the ones place. The point only looks like it hopped.
3Divide: Digits Move Right
45 ÷ 102 = 0.45
Dividing by two tens makes every digit worth a hundredth as much, so each moves two places right. The zero in the ones place says there are no ones. It is not decoration.
4A Zero Is Not a Ten
84.150
✗ zero tacked on
still 84.15
841.5
✓ every digit moved
84.15 × 10
Adding a zero opens a new ones place on a whole number. After a decimal it fills a place that was already empty, so nothing grows. Ask what each digit is worth.
