Multiplying a round number by a one-digit number

In the previous article we multiplied a round number by the same digit it began with. Now we go one step further: the second factor can be any digit from 1 to 9.

The rule stays the same

Again: multiply the leading digits and then append the right number of zeros.

Example 1: $300\cdot 7$

1. Times-tables: $3\cdot 7=21$.
2. The number 300 has 2 zeros.
3. Add 2 zeros to 21 → 2,100.

Example 2: $40\cdot 9$

1. Times-tables: $4\cdot 9=36$.
2. The number 40 has 1 zero.
3. Add 1 zero to 36 → 360.

Pattern in a table

This pattern shows why it works:

Each extra zero in the round number pushes one extra zero into the result.

Why some problems don't appear

The times-tables never give a result larger than 81. But once you append zeros, the product grows quickly — in our exercises the result always stays under 10,000, so it still fits in four digits.

For example:

• $3\cdot 3,000=9,000$ ✅ (fits)
• $4\cdot 3,000=12,000$ ❌ (larger than 9,999, never generated here)

Quick sanity check

The result should have as many zeros as the round number — when the product of the leading digits is two digits. When the product of the leading digits is a single digit (for example $2\cdot 3=6$), the number of zeros matches exactly: $2\cdot 300=600$.

Practice

👉 Exercise: Multiplying a round number

What comes next

• Once this feels easy, move on to column multiplication, where everything you've learned comes together: Column multiplication up to 10,000.
• Full overview: Topic guide.