Multiplying by 10, 100 and 1000

Why multiplying by 10, 100 and 1000 is special

Most multiplying takes effort. But multiplying by 10, 100 or 1000 is one of the fastest jobs in maths — once you know why it works.

These three numbers are special because our whole number system is built on groups of ten. You can read more about that in Place Value to Thousands. Each place is exactly ten times the place to its right.

The big idea: digits shift left

When you multiply a number by 10, every digit becomes ten times bigger. So every digit moves one place to the left into the next-bigger place.

Take 6. The 6 is in the ones place. Multiply by 10 and the 6 moves into the tens place — it is now worth 60.

But the ones place cannot be left blank. We put a 0 there as a place-holder. So:

6 × 10 = 60

The "extra zero" is really the place-holder that appears when the old ones place empties out.

Multiplying by 100 and 1000

The same idea repeats:

• × 10 = 1 shift left (10 is one ten)
• × 100 = 2 shifts left (100 = 10 × 10, two tens)
• × 1000 = 3 shifts left (1000 = 10 × 10 × 10, three tens)

So the number of zeros in 10, 100 or 1000 tells you how many places to shift.

Start	× 10	× 100	× 1000
3	30	300	3,000
8	80	800	8,000
12	120	1,200	12,000
25	250	2,500	25,000

Worked example 1: a single digit

Work out 7 × 100.

1. 100 has two zeros, so the digit shifts two places left.
2. The 7 starts in the ones place. Two shifts left lands it in the hundreds place → worth 700.
3. Fill the empty tens and ones places with zeros: 700.

So 7 × 100 = 700.

Worked example 2: a two-digit number

Work out 36 × 10.

1. 10 has one zero, so each digit shifts one place left.
2. The 3 moves from tens to hundreds (worth 300).
3. The 6 moves from ones to tens (worth 60).
4. A 0 fills the empty ones place.
5. Put it together: 300 + 60 + 0 = 360.

So 36 × 10 = 360.

Worked example 3: a number that already ends in zero

Work out 240 × 10.

This one catches people out, so go carefully.

1. Shift every digit one place left.
2. The 2 (hundreds) → thousands = 2,000.
3. The 4 (tens) → hundreds = 400.
4. The 0 (ones) → tens = 0.
5. A new 0 fills the empty ones place.
6. Total: 2,000 + 400 + 0 + 0 = 2,400.

So 240 × 10 = 2,400. We simply tacked one more zero onto the end — which matches the shortcut.

The shortcut and its trap

For whole numbers, here is the quick rule:

• × 10 → add one zero
• × 100 → add two zeros
• × 1000 → add three zeros

This works perfectly for whole numbers. But be careful: the shortcut does not work for decimals. For example, 3.5 × 10 is 35, not 3.50. You cannot just "add a zero" there. That is why it is safer to remember the real reason — digits shift left — because that rule always works.

Try it yourself

Solve these, then check the pattern.

• 9 × 10 = ? (Answer: 90)
• 9 × 100 = ? (Answer: 900)
• 9 × 1000 = ? (Answer: 9,000)
• 45 × 100 = ? (Answer: 4,500)

Then make up your own number and multiply it by all three. Say out loud how many places the digits shift each time.

Great job!

You can now multiply by 10, 100 and 1000 in seconds, and you understand the place-value reason behind it. This skill speeds up bigger multiplying too.

Next, learn the opposite move in Dividing by 10, 100 and 1000, or build fluency with your Times Tables.