Ross MackellUK-qualified primary teacher · 10 min read

Your child is asked 3.4 × 10. "Easy," they say. "You just add a zero." They write 3.40, and move on feeling pleased with themselves. The answer is 34.

"Just add a zero" is probably the most common maths shortcut parents pass on at home. It works perfectly for whole numbers, so it feels like a rule. Then decimals arrive in Year 4 and Year 5, and the shortcut quietly starts giving wrong answers, and nobody can see why.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you how UK schools teach multiplying and dividing by 10, 100 and 1000, why the digits move and the decimal point doesn't, how to handle zeros, and a 10-minute practice routine with answers.

What your child needs first

Multiplying and dividing by 10, 100 and 1000 is really a place value skill dressed up as a calculation. Before it clicks, your child needs:

• Place value, including tenths and hundredths. They should know that in 3.45, the 3 is worth 3 ones, the 4 is worth 4 tenths and the 5 is worth 5 hundredths. My guide to place value covers this.
• That each column is 10 times bigger than the one on its right. Ten ones make a ten, ten tens make a hundred, ten tenths make a one. This is the whole reason the method works.
• Partitioning. Being able to split 345 into 300 + 40 + 5 makes it obvious what happens to each part. See what is partitioning in maths?

In the national curriculum, Year 4 pupils find the effect of dividing a one- or two-digit number by 10 and 100. In Year 5 they multiply and divide whole numbers and decimals by 10, 100 and 1000, and by Year 6 they're expected to give answers up to three decimal places. Questions like 4.7 × 100 and 52 ÷ 1000 are regulars on the Year 6 SATs arithmetic paper.

Why "just add a zero" goes wrong

Here's the trouble with the shortcut. It works here:

• 34 × 10 = 340. Add a zero. Correct.
• 6 × 100 = 600. Add two zeros. Correct.

But it falls apart here:

• 3.4 × 10. Add a zero and you get 3.40, which is still 3.4. The answer is 34.
• 0.25 × 100. Add two zeros and you get 0.2500. The answer is 25.
• And it gives no help at all with dividing.

Adding a zero on the end of a decimal doesn't change its value at all. That's exactly why the shortcut breaks.

What's really happening when we multiply by 10 is that every digit becomes ten times bigger, so it moves one column to the left. With whole numbers, the empty ones column gets filled with a zero, so it looks like you added a zero. Teach your child the real reason and it works for every number they'll ever meet.

You might also have heard "move the decimal point". It gets the right answer, but UK schools teach that the digits move and the decimal point stays still. That matches what's really happening to the value of each digit, and it's what your child's teacher will say, so it's worth using the same language at home.

Multiplying by 10, 100 and 1000 step by step

The rule is simple: count the zeros, then move every digit that many places to the left.

• × 10: digits move 1 place left
• × 100: digits move 2 places left
• × 1000: digits move 3 places left

Example 1: 3.4 × 10

Write it in a place value chart. The 3 is in the ones column and the 4 is in the tenths.

The 3 ones become 3 tens. The 4 tenths become 4 ones. The decimal point hasn't moved at all. So 3.4 × 10 = 34. Quick sense check: 3 and a bit, ten times, is about 30-something. Yes.

Example 2: 0.56 × 100

Two zeros, so every digit moves two places left.

Money makes this one obvious: 56p is £0.56, and 100 lots of 56p is £56.

Example 3: 4.7 × 1000

Three zeros, three places left. This time there's a gap to fill.

The 4 moves from ones to thousands, and the 7 moves from tenths to hundreds. That leaves the tens and ones columns empty, so we fill them with zeros. 4.7 × 1000 = 4,700.

Dividing by 10, 100 and 1000 step by step

Dividing is the same idea in reverse. Count the zeros, then move every digit that many places to the right. The number gets smaller.

Example 4: 45 ÷ 10

4 tens become 4 ones, and 5 ones become 5 tenths. 45 ÷ 10 = 4.5. Notice the whole number 45 had a decimal point all along. It was just hiding after the 5.

Example 5: 362 ÷ 100

This is exactly what happens when you turn 362p into pounds: £3.62. If your child is comfortable with money, start there.

Example 6: 7 ÷ 1000

The 7 moves three places right, from ones to thousandths. Everything in between needs a zero, and so does the ones column, because we never start a decimal with just a dot. 7 ÷ 1000 = 0.007.

What to do with zeros

Zeros cause most of the confusion with this skill, so here are the three rules I give children:

1. Fill gaps before the decimal point with zeros. 4.7 × 1000 needs two zeros to make 4,700. Without them, the 4 and 7 slide back into the wrong columns.
2. Fill gaps straight after the decimal point with zeros. 7 ÷ 1000 is 0.007, not 0.7. Those zeros are doing a job.
3. Zeros on the very end of a decimal can go. 3.6 × 100 = 360, but 360 ÷ 100 is 3.60, which we just write as 3.6. Both are correct.

A zero that holds a digit in its column is called a placeholder. If your child hears that word at school, that's what it means.

Watch me teach place value

Everything in this guide rests on place value. This video shows how I explain it to children, and why each column is worth ten times the one next to it:

Where this skill turns up

Once your child has this, a surprising amount of maths gets easier.

• Multiplying by multiples of 10. 30 × 4 is just 3 × 4 = 12, then × 10 = 120. And 30 × 40 is 3 × 4 × 100 = 1,200. This is pure times tables plus place value.
• Long multiplication. That mysterious zero on the second line of long multiplication is there because you're multiplying by tens. Children who understand × 10 never forget it.
• Percentages. Finding 10% means dividing by 10, and 1% means dividing by 100. See how to work out percentages.
• Converting units. 2.5 kg is 2,500 g (× 1000). 340 cm is 3.4 m (÷ 100). £4.25 is 425p (× 100). This comes up constantly in Year 5 and Year 6 word problems.

4 common mistakes and how to fix them

Mistake 1: "Just add a zero" with a decimal

3.4 × 10 = 3.40. The number hasn't changed at all.

The fix: always estimate first. "Ten lots of about 3 is about 30. Is 3.40 about 30?" Then use a place value chart until the digits moving feels natural.

Mistake 2: Moving the wrong way

Your child divides 45 by 10 and gets 450.

The fix: one question before every calculation: "Will the answer be bigger or smaller?" Multiplying by 10 makes a number bigger, dividing makes it smaller. If the answer went the wrong way, they'll spot it straight away.

Mistake 3: Moving the wrong number of places

5.2 × 100 becomes 52, because they only moved one place.

The fix: count the zeros out loud and tap a finger for each one as they move. 100 has two zeros, so two taps, two places. 5.2 × 100 = 520.

Mistake 4: Losing the placeholder zeros

7 ÷ 1000 is written as 0.7, or 4.7 × 1000 as 47.

The fix: use squared paper with the columns labelled, at least at first. When the gap is right there in front of them, they're far more likely to fill it.

A 10-minute practice routine

Same three steps I use for every skill: watch, copy, practise.

1. Watch: do one example yourself, out loud. "Times 100. Bigger. Two zeros, so two places left."
2. Copy: your child does a very similar one, saying the same three things.
3. Practise: three or four on their own. Then check each one with the inverse: if 3.4 × 10 = 34, then 34 ÷ 10 should be 3.4.

Only move on when they're getting three in a row right. If they keep getting the direction wrong, go back to estimating. If they keep losing zeros, go back to the place value chart. Ten minutes, a few times a week, is plenty.

Frequently asked questions

How do you multiply by 10, 100 and 1000?

Move every digit to the left: one place for 10, two places for 100 and three places for 1000. The decimal point stays where it is. Fill any empty columns before the decimal point with zeros. For example, 4.7 × 100 = 470.

How do you divide by 10, 100 and 1000?

Move every digit to the right: one place for 10, two places for 100 and three places for 1000. The number gets smaller. If there are empty columns straight after the decimal point, fill them with zeros. For example, 52 ÷ 1000 = 0.052.

Why is "just add a zero" wrong?

It only works for whole numbers. Adding a zero to the end of a decimal doesn't change its value, so 3.4 with a zero added is still 3.4, but 3.4 × 10 is 34. Teaching children that the digits move one place for every zero works for every number.

Does the decimal point move when you multiply by 10?

In UK primary schools, children are taught that the digits move and the decimal point stays still. Moving the decimal point gives the same answer, but moving the digits shows what is really happening: each digit becomes ten times bigger or smaller.

What year do children learn to multiply and divide by 10, 100 and 1000?

Children divide one- and two-digit numbers by 10 and 100 in Year 4. In Year 5 they multiply and divide whole numbers and decimals by 10, 100 and 1000, and in Year 6 they give answers with up to three decimal places. It appears regularly in the SATs arithmetic paper.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (Years 4 to 6)
• Oak National Academy, Multiplying and dividing by 10, 100 and 1,000 (free pupil lesson)
• NCETM, Year 5: Calculating with decimal fractions
• Ross Mackell, Teacher's Perspective on YouTube