You know that each place is ten times the next. So multiplying by 10 slides every digit one place to the left. Multiplying by 100 is two slides, and by 1,000 is three.
Key idea
$n \times 10$, $n \times 100$ and $n \times 1{,}000$ move every digit of $n$ one, two or three places left, with zeros filling the empty places. For $6 \times 400$, use the fact $6 \times 4 = 24$: the answer is 24 hundreds, $2{,}400$.
Why it works
$47 \times 10$ is 10 groups of 47: 10 groups of 4 tens is 40 tens (4 hundreds), and 10 groups of 7 ones is 7 tens. So 4 moves to the hundreds and 7 to the tens: $470$. Each digit lands one place higher. The zero is not "added on"; it holds the empty ones place.
Worked example: A power of ten
Find $36 \times 1{,}000$.
- $1{,}000$ is $10 \times 10 \times 10$, so the digits move 3 places left.
- 36 ones become 36 thousands.
Answer: $36{,}000$
Worked example: A basic fact with tens and hundreds
Find $50 \times 400$.
- Basic fact: $5 \times 4 = 20$.
- Tens times hundreds make thousands, so the product is 20 thousands.
- 20 thousands is $20{,}000$.
Answer: $20{,}000$
Common mistake
Counting zeros carelessly. In $50 \times 400$, the fact $5 \times 4 = 20$ already ends in 0, so the answer $20{,}000$ has four zeros, not three. Say it in units ("20 thousands") to check.