Multiplying and Dividing Decimals KS2: Complete Guide with Free Worksheets
By 10, 100 and 1000 · Place Value Method · SATs Tips · Free Worksheets Years 4–6 · Last updated June 2026 · Written by the Kwized team and reviewed against the KS2 National Curriculum for Mathematics
What Does Multiplying and Dividing Decimals by 10, 100 and 1000 Mean?
When you multiply or divide a decimal by 10, 100, or 1000, the digits stay the same but their position in the place value chart shifts. Multiplying moves every digit to the left (the number gets bigger); dividing moves every digit to the right (the number gets smaller). The decimal point itself never moves — the digits move around it.
Example: 3.45 × 10 = 34.5 — every digit shifts one place to the left.
Example: 3.45 ÷ 100 = 0.0345 — every digit shifts two places to the right.
The Place Value Chart: The Only Tool You Need
The single most effective way to teach multiplying and dividing decimals is the place value chart. Every calculation in this topic can be solved by asking one question: how many places do the digits move, and in which direction?
A common but misleading shortcut is telling children to “move the decimal point.” The decimal point never moves. It always sits between the ones and tenths columns. What moves are the digits — left when multiplying, right when dividing. Teaching this correctly from the start prevents place value confusion in Years 5 and 6.
Multiplying Decimals: Digits Move Left
| Calculation | Digit movement | Result | How to read it |
|---|---|---|---|
| 3.45 × 10 | 1 place left | 34.5 | 34 and five-tenths |
| 3.45 × 100 | 2 places left | 345 | three hundred and forty-five |
| 3.45 × 1000 | 3 places left | 3450 | three thousand four hundred and fifty |
| 0.07 × 10 | 1 place left | 0.7 | seven-tenths |
| 0.07 × 100 | 2 places left | 7 | seven |
| 0.07 × 1000 | 3 places left | 70 | seventy |
| 0.6 × 10 | 1 place left | 6 | six |
| 1.8 × 100 | 2 places left | 180 | one hundred and eighty |
Dividing Decimals: Digits Move Right
| Calculation | Digit movement | Result | How to read it |
|---|---|---|---|
| 34.5 ÷ 10 | 1 place right | 3.45 | three and forty-five hundredths |
| 345 ÷ 100 | 2 places right | 3.45 | three and forty-five hundredths |
| 3450 ÷ 1000 | 3 places right | 3.45 | three and forty-five hundredths |
| 7 ÷ 10 | 1 place right | 0.7 | seven-tenths |
| 7 ÷ 100 | 2 places right | 0.07 | seven-hundredths |
| 7 ÷ 1000 | 3 places right | 0.007 | seven-thousandths |
| 56 ÷ 100 | 2 places right | 0.56 | fifty-six hundredths |
| 4.2 ÷ 1000 | 3 places right | 0.0042 | forty-two ten-thousandths |
SATs arithmetic papers frequently include chains like 3.6 × 100 ÷ 10. Teach children to work left to right — multiply first (3.6 × 100 = 360), then divide (360 ÷ 10 = 36). Doing both steps on one place value chart in one go is faster and less error-prone than two separate calculations.
Multiplying and Dividing Decimals by Year Group
| Year Group | Key Objectives | NC Reference |
|---|---|---|
| Year 4 | Divide one- and two-digit numbers by 10 and 100; identify the value of digits in decimal numbers (tenths and hundredths) | NC Maths Year 4 — Fractions (including decimals) |
| Year 5 | Multiply and divide whole numbers and decimals by 10, 100, and 1000; read, write, order, and compare numbers with up to three decimal places | NC Maths Year 5 — Fractions (including decimals and percentages) |
| Year 6 | Multiply and divide numbers by 10, 100, and 1000 in multi-step reasoning problems; use this skill in fraction, percentage, and measurement contexts; apply to SATs reasoning questions | NC Maths Year 6 — Fractions (including decimals and percentages) |
5 Common Mistakes and How to Fix Them
| Mistake | ❌ Incorrect | ✅ Fix |
|---|---|---|
| Moving the decimal point | “Move the point one place” → 3.4 × 10 = 3.40 | Move the DIGITS left. 3.4 × 10 = 34 |
| Forgetting the zero placeholder | 7 ÷ 100 = .7 | 7 ÷ 100 = 0.07 — always write the leading zero |
| Wrong number of places | 3.45 × 100 = 34.5 (only moved one place) | × 100 = 2 places left → 345. Count the zeros in 100. |
| Confusing × and ÷ direction | Dividing but moving digits left, making the number bigger | Multiply = bigger = left. Divide = smaller = right. Always sense-check the answer size. |
| Dropping digits when crossing columns | 0.05 × 10 = 0.5 but child writes 5. (missing the decimal) | Always write the full number including decimal point: 0.5, not 5 — unless digits have genuinely moved past the ones column. |
3 Classroom & Home Strategies
Strategy 1 — The Place Value Slider. Draw a place value chart on card and write a number on a strip of paper that slides left and right through it. Physically sliding the digits one, two, or three places while calling out “times ten, times hundred, times thousand” builds the kinaesthetic memory that abstract practice alone can’t.
Strategy 2 — The Sense Check. After every calculation, ask: “Is this number bigger or smaller than what we started with?” Multiplying should always give a bigger result; dividing should always give a smaller one. This one habit catches the majority of errors before they become ingrained.
Strategy 3 — The Daily Kwized Quiz. A focused five-to-ten-question quiz on multiplying and dividing decimals, taken daily, builds the automatic recall that SATs conditions require. Kwized’s interactive quiz below gives instant feedback so wrong answers become teaching moments rather than missed opportunities.
Free Kwized KS2 Decimals Worksheets (PDF)
Three curriculum-aligned worksheets covering multiplying and dividing decimals by 10, 100, and 1000 — one for each year group. Each includes a full answer key. Free to download and use in the classroom or at home.
Tenths & HundredthsDividing one- and two-digit numbers by 10 and 100. Place value chart practice and identifying tenths and hundredths.
Full Range PracticeMultiplying and dividing decimals by 10, 100, and 1000. Up to three decimal places. SATs-style question formats.
Multi-Step ReasoningMulti-step problems applying decimal multiplication and division in measurement, fraction, and percentage contexts.
Kwized subscribers get access to additional worksheets, adaptive quizzes, and progress tracking across every KS2 maths topic.
Interactive KS2 Decimals Quiz — Free Practice
Test your knowledge of multiplying and dividing decimals with this free Year 5 interactive practice quiz. Pupils move digits on a place value chart, complete multiplication and division calculations, and answer SATs-style questions — with instant feedback on every answer. No login required to play.
This quiz covers multiplying and dividing decimals by 10, 100, and 1000 — a key objective in the KS2 National Curriculum for Mathematics tested in both the arithmetic and reasoning SATs papers. Register free to save your score, track progress, and access the full Kwized question bank.
Real-World Decimal Contexts for the Classroom
Children retain this skill far better when they see why it matters. Multiplying and dividing decimals by 10, 100, and 1000 appears constantly in everyday maths:
| Context | Real-world example | Calculation involved |
|---|---|---|
| Money | Converting pence to pounds | 450p ÷ 100 = £4.50 |
| Measurement | Converting mm to cm | 35mm ÷ 10 = 3.5cm |
| Measurement | Converting cm to m | 275cm ÷ 100 = 2.75m |
| Measurement | Converting m to km | 1500m ÷ 1000 = 1.5km |
| Science | Converting g to kg | 750g ÷ 1000 = 0.75kg |
| Sport | Race time in seconds to milliseconds | 9.58s × 1000 = 9580ms |
Key Vocabulary Glossary
| Term | Definition |
|---|---|
| Decimal | A number with digits after the decimal point representing parts of a whole |
| Decimal point | The dot separating the whole number part from the fractional part; it never moves |
| Place value | The value of a digit based on its position in a number (thousands, hundreds, tens, ones, tenths, hundredths) |
| Tenths | The first column after the decimal point; one-tenth = 0.1 = 1/10 |
| Hundredths | The second column after the decimal point; one-hundredth = 0.01 = 1/100 |
| Thousandths | The third column after the decimal point; one-thousandth = 0.001 = 1/1000 |
| Placeholder zero | A zero inserted to maintain correct place value, e.g. 0.07 — the zero in the tenths column holds the place |
| Digit | Any of the symbols 0–9; in place value, digits move position when multiplying or dividing by powers of 10 |
| Power of 10 | 10, 100, 1000 etc — each is 10 multiplied by itself a number of times; determines how many places digits shift |
| Arithmetic paper | The KS2 SATs paper testing calculation skills including decimal multiplication and division |
| Reasoning paper | The KS2 SATs paper testing problem-solving and application of decimal skills in context |
Related KS2 Maths Topics
Frequently Asked Questions
Move every digit one, two, or three places to the left on a place value chart — one place for ×10, two for ×100, three for ×1000. The decimal point stays fixed between the ones and tenths columns. Example: 3.45 × 100 = 345 — digits move two places left.
Move every digit one, two, or three places to the right — one place for ÷10, two for ÷100, three for ÷1000. Add zero placeholders as needed. Example: 7 ÷ 100 = 0.07 — digits move two places right, requiring a zero placeholder in the tenths column.
No — the decimal point never moves. It always sits between the ones and tenths columns. What moves are the digits, left when multiplying and right when dividing. Teaching children to say “the digits move” rather than “the point moves” prevents the most common place value error in KS2.
Dividing by 10 and 100 is introduced in Year 4. The full range — multiplying and dividing by 10, 100, and 1000 with decimals to three places — is taught in Year 5 and applied to multi-step reasoning in Year 6 SATs preparation.
Two places to the left. A useful rule: count the zeros in the number you are multiplying or dividing by — that tells you how many places to move. 10 has one zero → one place. 100 has two zeros → two places. 1000 has three zeros → three places.
Yes — in both the arithmetic paper and the reasoning papers. The arithmetic paper tests direct calculation (e.g. 4.6 × 100). The reasoning papers apply the skill in context — unit conversions, money problems, and multi-step questions. It is one of the most reliably tested decimal skills across all three SATs papers.
A placeholder zero is a zero inserted to maintain correct place value when digits move. For example, 7 ÷ 100 = 0.07 — the zero in the tenths column is a placeholder holding the position so the 7 correctly sits in the hundredths column. Without it, the answer would be misread as 0.7.
Tenths are the first column after the decimal point (0.1 = 1/10). Hundredths are the second column (0.01 = 1/100). Thousandths are the third column (0.001 = 1/1000). Each column is ten times smaller than the one to its left.
