You know that each place is ten times the place to its right: one, ten, hundred, thousand. Writing $10 \times 10 \times 10 \times 10$ for ten thousand takes a while, so there is a short way: an exponent.
Key idea
$10^{3}$ means $10 \times 10 \times 10 = 1{,}000$. The small raised number, the exponent, says how many 10s are multiplied. $10^{n}$ is a 1 followed by $n$ zeros.
Why it works
Each time you multiply by 10, every digit moves one place to the left and a 0 fills the ones place. Start with 1 and multiply by 10 three times: $10$, then $100$, then $1{,}000$. Three factors of 10, three zeros.
| Power | Product | Value |
|---|---|---|
| $10^{1}$ | $10$ | $10$ |
| $10^{2}$ | $10 \times 10$ | $100$ |
| $10^{3}$ | $10 \times 10 \times 10$ | $1{,}000$ |
| $10^{4}$ | $10 \times 10 \times 10 \times 10$ | $10{,}000$ |
Worked examples
Worked example: Value of a power
What is $10^{5}$?
- Five 10s multiplied: $10 \times 10 \times 10 \times 10 \times 10$.
- That is a 1 with five zeros.
Answer: $100{,}000$
Worked example: A number times a power of ten
What is $6 \times 10^{3}$?
- $10^{3} = 1{,}000$.
- $6 \times 1{,}000 = 6{,}000$: the 6 moves three places left.
Answer: $6{,}000$
Common mistake
Reading $10^{3}$ as $10 \times 3 = 30$. The exponent is not a factor; it counts factors. Check: $10^{3}$ must be bigger than $10^{2} = 100$, and 30 is not.