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Level 4Grade 4skill: multiply_by_10s· 7 min read

Multiplying by 10, 100 and 1000

In short: Multiplying by 10, 100 or 1000 shifts every digit one, two or three places to the left — the zeros just fill the gaps. Multiply the front digits, then write one zero for each zero in the multiplier, and never drop a zero that comes out of the multiplication itself.

How to multiply by 10, 100 and 1000

Multiplying by 10 does not add a zero — it shifts every digit one place to the left. A single 3 becomes 30; the value gets ten times bigger, so it slides up into the tens column. Multiplying by 100 shifts two places, and by 1000 shifts three places. Writing a zero is just how you fill the empty column the shift leaves behind.

For a whole number, that shift shows up as extra zeros on the end. Count the zeros in the number you are multiplying by: 10 has one zero, 100 has two, 1000 has three. Write exactly that many zeros after your number — each one marks a column the shift has emptied.

When both numbers are round — like 40 × 300 — do the same thing in two clean steps. Multiply the non-zero front digits (4 × 3 = 12), then tack on every zero from both numbers (one from 40, two from 300, so three zeros): 12000.

  1. Look at how many zeros are in 10, 100 or 1000 — that is one, two or three.
  2. Multiply the leading digits as a normal times-tables fact.
  3. Write that answer, then add one zero for each zero in the multiplier — each zero marks a column the shift has emptied.
  4. For two round numbers, add up the zeros from both and write them all after the leading product.
  5. Check: does the answer look about the right size? 8 × 100 should be in the hundreds, not the thousands.

Why the shift trick always works Why it works

× 10
Every digit moves one place left; write one zero to mark the emptied column.

46 × 10 = 460

× 100
Digits move two places left; write two zeros.

46 × 100 = 4600

× 1000
Digits move three places left; write three zeros.

46 × 1000 = 46000

round × round
Multiply the front digits, then write every zero from both numbers.

40 × 300 = 12000 (4 × 3, then three zeros)

trailing-zero trap
If the front product itself ends in a zero, that zero counts too — do not lose it.

50 × 40 = 2000 (5 × 4 = 20, then two more zeros)

This is why the trick survives place value: you are always moving digits, never inventing them. That is also why it keeps working with decimals later — 4.6 × 10 = 46 — where 'just add a zero' would give you the wrong answer.

Worked examples

7 × 10 = 70
  1. 10 has one zero.
  2. 7 × 1 = 7, then write one zero.
34 × 100 = 3400
  1. 100 has two zeros.
  2. Keep the 34, then write two zeros.
6 × 1000 = 6000
  1. 1000 has three zeros.
  2. 6, then three zeros.
80 × 30 = 2400
  1. Front digits: 8 × 3 = 24.
  2. Zeros: one from 80, one from 30 — that is two zeros.
  3. Write 24, then two zeros.
50 × 40 (the trap) = 2000
  1. Front digits: 5 × 4 = 20 — notice this already ends in a zero.
  2. Now add the two zeros from 50 and 40.
  3. So it is 20 followed by two more zeros — three zeros in all.
700 × 6 = 4200
  1. Front digits: 7 × 6 = 42.
  2. Zeros: two from 700.
  3. Write 42, then two zeros.

Common mistakes

One zero too many

✗ 8000

For 8 × 100 the student wrote three zeros, but 100 only has two. One extra zero makes the answer ten times too big.

Fix: Count the zeros in the multiplier before you write anything. 100 has exactly two zeros, so 8 × 100 = 800.

off_by_one

A slip in the times-table fact

✗ 210

For 6 × 30 the student recalled 6 × 3 as 21 (that is really 7 × 3). The zero-rule was applied correctly to a wrong fact.

Fix: Lock the fact first: 6 × 3 = 18. Then attach the zero: 6 × 30 = 180.

table_neighbour

Divided instead of multiplied

✗ 80

For 800 × 10 the student made the number smaller, dividing 800 by 10. Multiplying by 10 makes numbers bigger, not smaller.

Fix: Multiplying by 10 makes a number bigger — every digit shifts one place up, so 800 × 10 = 8000.

wrong_operation

Shifted the wrong number of places

✗ 250

For 25 × 100 the student shifted only one place, treating × 100 like × 10. That is a two-place shift, so it needs two zeros.

Fix: × 100 means move two places and write two zeros: 25 × 100 = 2500.

place_value_slip

Practice: multiply by 10s

Work through these. Watch for the trailing-zero trap, and count the zeros in the multiplier before you write your answer.

Related skills

First, make sure of

Frequently asked questions

Does multiplying by 10 really just add a zero?

For whole numbers it looks that way, but the real rule is that every digit shifts one place to the left. The zero just fills the empty column. Thinking 'shift', not 'add a zero', is what keeps you right when decimals show up later — 4.6 × 10 = 46, not 4.60.

How many zeros do I write for something like 40 × 300?

Add up the zeros from both numbers: 40 has one and 300 has two, so three zeros in total. Multiply the front digits (4 × 3 = 12) and write all three zeros after: 40 × 300 = 12000.

Why does 50 × 40 have three zeros when I only see two?

Because the front product carries its own zero. 5 × 4 = 20, which already ends in a zero, and then you still add the two zeros from 50 and 40. That gives 2000. Never drop a zero that comes out of the multiplication itself.

What is the most common mistake with these questions?

Miscounting zeros — writing one too many or one too few. Before you write your answer, count the zeros in the multiplier (10 has one, 100 has two, 1000 has three) and make sure your answer has exactly that many extra.

How do I check my answer is sensible?

Think about size. 8 × 100 should land in the hundreds, so 800 is reasonable while 8000 is clearly too big. A quick size check catches most zero-counting slips.