Multiplying and dividing by 10, 100 and 1000 explained for parents (Australia)

Ask most adults how to multiply by 10 and you'll hear the same shortcut: just add a zero. It works for 46 × 10 = 460, so it sticks. Then your Year 5 or 6 child brings home 2.5 × 10, writes 2.50, and can't understand why it's marked wrong. The shortcut didn't fail because your child was careless; it failed because it never described what was actually happening to the number.

What really happens is simple and worth getting right: when you multiply by 10, every digit becomes ten times bigger in value, so each one moves one place to the left on the place-value chart. Multiply by 100 and the digits move two places; by 1000, three places. Dividing by 10, 100 or 1000 moves the digits the other way. The decimal point itself stays put.

Below: whole numbers, then decimals, then where it turns up in real life — centimetres, cents, 10% off. If tens, ones and tenths feel shaky, warm up with place value first.

Why "add a zero" is a trap

The zero shortcut is a pattern children spot, not a rule they understand:

Question	"Add/remove a zero" gives	Correct answer	What went wrong
46 × 10	460	460	Nothing — whole numbers happen to work
2.5 × 10	2.50	25	2.50 is the same value as 2.5; nothing got bigger
35 ÷ 10	??? (no zero to remove)	3.5	The shortcut has no answer at all
7 ÷ 100	0.7 (a common guess)	0.07	Only moved one place instead of two

Only the first row comes out right. That's why teachers now talk about digits moving places: one idea that works for every row, and keeps working into secondary school. (Some classes say "the decimal point moves" instead. Same answer — if that's your child's teacher's language, use it at home.)

Seeing it on a place-value chart

A place-value chart lets you watch it happen. Rule columns on a strip of paper, write digits on small cards and slide them.

First, the zeros aren't "added" for fun. When 46 slides two places left, the tens and ones columns are left empty, and a zero sits in each so the 4 and 6 stay in the thousands and hundreds — the job described in zero holds the place.

Second, 3.7 × 10 needs no zero at all. The 3 moves into the tens, the 7 moves from tenths into ones, and you get 37. No empty column, nothing to fill.

Dividing: the same move in reverse

Division by 10, 100 or 1000 makes every digit ten, a hundred or a thousand times smaller, so the digits slide to the right.

• 520 ÷ 10 = 52 (one place right)
• 520 ÷ 100 = 5.2 (two places; the 2 lands in the tenths)
• 520 ÷ 1000 = 0.52 (three places; a zero goes in the ones so the point isn't left floating)
• 35 ÷ 10 = 3.5
• 7 ÷ 100 = 0.07 — the 7 moves two places right, from ones to hundredths, and a zero must hold the tenths
• 63 ÷ 1000 = 0.063

Most errors creep in with 7 ÷ 100. If your child writes 0.7, count the jumps together on the chart: ones → tenths is one, tenths → hundredths is two. The empty tenths column needs its zero.

Multiples of ten: where the real payoff is

Once the move is solid, children can split harder sums into a times-table fact plus a powers-of-ten step:

• 30 × 4 = 3 × 4 × 10 = 12 × 10 = 120
• 40 × 60 = 4 × 6 × 10 × 10 = 24 × 100 = 2400
• 300 × 20 = 3 × 2 × 100 × 10 = 6 × 1000 = 6000
• 2400 ÷ 60 → think 240 ÷ 6 = 40

In Year 6 the same thinking stretches to decimals:

• 0.3 × 20 = 0.3 × 2 × 10 = 0.6 × 10 = 6
• 1.2 × 300 = 1.2 × 3 × 100 = 3.6 × 100 = 360
• 4.8 ÷ 40 = 4.8 ÷ 4 ÷ 10 = 1.2 ÷ 10 = 0.12

All of these lean on times tables: if 4 × 6 still needs fingers, the fact is the bottleneck, not the tens. The same skill hides inside the "× 20" row of long multiplication and the "how many 40s?" steps of long division.

Where it turns up outside the maths book

The metric system and our money are both built on tens, which makes this one of the most practical ideas in primary maths.

Measurement. A metre is 100 centimetres and a kilogram is 1000 grams, so converting is mostly × or ÷ by 10, 100 or 1000:

• 3.5 m = 3.5 × 100 = 350 cm
• 85 cm = 85 ÷ 100 = 0.85 m
• 2400 g = 2400 ÷ 1000 = 2.4 kg
• 1.25 L = 1.25 × 1000 = 1250 mL

Check with "should there be more of the smaller unit?" — always more centimetres than metres. See converting units, plus length, mass and capacity.

Money. Ten pies at $4.50 each cost $4.50 × 10 = $45.00. A hundred stickers at $2.35 a sheet would be $235. Splitting a $120 bill between ten friends is $120 ÷ 10 = $12 each. Money maths at home has more ways to use the shopping trip.

Percentages. Finding 10% of something is just dividing by 10. Ten per cent off a $45 jumper saves $4.50. That makes ÷10 the quiet engine behind a lot of percentages of amounts.

What the Australian Curriculum says

In version 9 of the Australian Curriculum: Mathematics, the idea arrives in two stages. In Year 4, students solve problems that involve multiplying or dividing whole numbers by multiples and powers of 10 without a calculator, using how the value of a digit changes from one place to the next. By Year 6, they do the same with decimals, drawing on place value and multiplication facts, and use estimation and rounding to check their answers make sense.

Victoria's Curriculum 2.0 tracks version 9 closely, so timing there is similar. Within that, schools pick their own models — a chart in one class, base-ten blocks or a calculator investigation in another.

How it usually builds, Prep to Year 6

Prep–Year 3: counting by tens, bundling ten ones into a ten, place value to the thousands and early patterns like 4 × 10 = 40 — groundwork rather than formal ×10. Overviews: Year 2, Year 3.

Year 4: whole numbers × and ÷ by 10 and 100 (and multiples like 30 or 200), plus first contact with tenths and hundredths. Overview: Year 4.

Year 5: wider use with larger whole numbers, estimating with rounding, and connecting tenths and hundredths to decimals in measurement. Overview: Year 5.

Year 6: decimals × and ÷ by 10, 100, 1000 and their multiples, unit conversions, money and percentage problems. Overview: Year 6.

A term either side of these markers is perfectly normal.

Helping at home: talk about value, not zeros

The most useful thing you can do is change the language. Instead of "add a zero", try:

• "What's each digit worth now?"
• "Did the number get bigger or smaller? So which way should the digits go?"
• "How many places is that — one for ten, two for a hundred, three for a thousand?"
• "Is there an empty column that needs a zero to hold it?"
• "Does the answer feel about right?"

If your child already relies on "add a zero", don't ban it. Show a decimal case where it fails and let them work out why; children keep an idea better when they've found its limits themselves.

Three or four questions with real discussion beat a page of rushed answers. If it gets tense, stop and return another day (homework without tears has calm ways to reset).

Five quick games

1. Slide rule — call "times 100!" or "divide by 10!" and your child slides digit cards along a paper chart, adding zero cards only where a column is empty.
2. Calculator detective — type 0.6 × 10, 0.6 × 100, 0.6 × 1000 and have your child describe the pattern before you explain anything.
3. Shop owner — set a price; the other player costs 10, 100 or 1000 of them. Then reverse it: "A box of 100 costs $350. How much is one?" ($3.50)
4. Tape measure swap — measure household things in centimetres, then convert: the fridge at 178 cm becomes 1.78 m.
5. Bigger or smaller? — call out 45 ÷ 100 and your child shouts "smaller!" before working it out. Direction sense catches most errors.

Mistakes that come up again and again

Adding a zero after a decimal. 2.5 × 10 written as 2.50. Ask, "Is 2.50 any bigger than 2.5?" The answer (no) usually does the teaching.

Moving the wrong way. 520 ÷ 10 written as 5200. A quick "should sharing make it bigger?" check helps.

Moving the wrong number of places. Using one place for ×100. Link places to the zeros in the multiplier: 100 has two zeros, so two places.

Losing the placeholder. 7 ÷ 100 written as 0.7 instead of 0.07, or 46 × 100 written as 460. Point to the empty column and ask what lives there.

Tables slips in multiples of ten. 40 × 60 = 2000 because 4 × 6 was recalled as 20. The powers-of-ten step was right; the fact wasn't. Practise the fact separately.

When to ask for more support

If, after several weeks of short, relaxed practice, your child still can't say which way the digits move — or place value in general is the sticking point — show the class teacher a page of their working and ask which language and models the class uses.

If the worry is bigger than this one topic, start with Is my child behind in maths?, then read about anxiety around maths or when maths struggles need attention. This page is general information and can't assess your child; persistent difficulties deserve a proper look from the school or a trained professional.

FAQ

What happens when you multiply by 10?

Each digit becomes worth ten times as much, so it moves one place to the left on a place-value chart. If a column is left empty, a zero holds it.

Why can't my child just add a zero?

It only works for whole numbers. With decimals (2.5 × 10) it gives a wrong answer, and it doesn't help with division at all.

Does the decimal point move or do the digits move?

Strictly, the digits move and the point stays between the ones and tenths. Some teachers describe it as the point moving; both give the same answer, so follow your child's class.

What year do kids learn to multiply decimals by 10, 100 and 1000?

In the Australian Curriculum (v9), whole numbers come in Year 4 and decimals in Year 6, although schools pace it differently.

Your next move

This week, grab a receipt, recipe or tape measure and ask one "times ten" and one "divided by a hundred" question about it. If your child can explain which way the digits went, and why, they understand more than any shortcut could teach.

If you'd like a wider look at where your child's number sense is sitting right now, Ziado has a free check you can do at home. It's a single adaptive diagnostic that runs for about ten minutes and shows a partial set of results — there's no account to create and no card details to give; signing up is what opens the full placement. It won't grade this one topic, it isn't NAPLAN preparation, and it isn't a medical or learning assessment. You can read about ongoing practice on the Ziado maths page, where Individual and Family plans each start with a 14-day free trial; plan details are on pricing.