Multiplying a round number by the same digit

Multiplying a round number by the same digit

This is the easiest step in the topic of multiplication by a one-digit number. Go through it carefully — it gives you the confidence you need for every problem that follows.

What is a round number?

A round number is a number that has a single non-zero digit at the start, with only zeros behind it:

3
30
300
3,000

All of these numbers share the same leading digit (3). They differ only in the number of zeros.

The key idea

If you know that 3 · 3 = 9, you also know the answer for every round number that begins with 3:

3 · 3=9
3 · 30=90
3 · 300=900
3 · 3,000=9,000

The number of zeros in the result is the same as the number of zeros in the round number. That's the whole trick.

Step-by-step approach

  1. Multiply the leading digits — use the basic times-tables.
  2. Count the zeros in the round number.
  3. Append that many zeros to the product.

Example

Compute :

  1. Times-tables: .
  2. The number 500 has 2 zeros.
  3. Add 2 zeros to 25 → 2,500.

Why it works

A round number can be split into a digit times a power of ten (tens, hundreds, thousands):

Then we rearrange the order of multiplication:

That's why multiplying the leading digits and then appending zeros gives the correct answer.

Watch out for

  • Don't drop any zero. (two zeros), not 90.
  • You need the times-tables by heart. Without them, every multi-digit problem is slow.

Practice

👉 Exercise: Multiplying a round number by the same digit

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