Multiplying and dividing by 10, 100 and 1,000: what children learn
This sprint includes whole numbers and decimals, such as 3.7 × 100 = 370 and 45 ÷ 1,000 = 0.045. Answers never have more than three decimal places, matching the curriculum. You can type answers with or without commas (both 4,500 and 4500 are accepted).
Supplemental place-value practice with powers of ten; a useful connection to 5.NBT.A.2, not full coverage of that standard.
How to play
How many can you answer in 60 seconds? Type the answer and press Enter. Questions keep coming for 60 seconds. Type each answer and press Enter, or choose Skip. Answers can be typed with or without commas.
Step by step
- Think about place value, not 'adding zeros'. When you multiply by 10, each digit moves one column to the left: 3.7 becomes 37. The decimal point stays still; the digits move.
- Count the zeros in 10, 100 or 1,000. 10 has one zero, so the digits move 1 place. 100 has two zeros: 2 places. 1,000 has three: 3 places.
- Multiply makes bigger, divide makes smaller. Check the direction: × 100 should give a much bigger number, ÷ 100 a much smaller one.
- Use zeros as place holders. 4.7 × 100: the 4 moves to the hundreds and the 7 to the tens, so a 0 fills the ones place: 470. For 45 ÷ 1,000, zeros fill the empty decimal places: 0.045.
Worked examples
Example 1: 3.7 × 100 = ?
Working: Each digit moves two places left: 3 ones becomes 3 hundreds, 7 tenths becomes 7 tens.
Answer: 370
Example 2: 560 ÷ 10 = ?
Working: Each digit moves one place right.
Answer: 56
Example 3: 2.5 ÷ 100 = ?
Working: Each digit moves two places right: 2 ones becomes 2 hundredths, 5 tenths becomes 5 thousandths.
Answer: 0.025
Common mistakes and how to fix them
- 'Adding a zero' to decimals: 3.5 × 10 written as 3.50. Adding a zero to the end of a decimal doesn't change its value. Use a place value chart and move the digits instead.
- Moving the digits the wrong way when dividing. Ask 'should the answer be bigger or smaller?' before writing it.
- Losing the leading zero: 0.045 written as .45 or 0.45. Count the places carefully on a chart with ones, tenths, hundredths and thousandths columns.
Activities to try at home
- Convert units: 3.5 kg is 3,500 g (× 1,000), 250 cm is 2.5 m (÷ 100).
- Work out the cost of 10 or 100 items at a given price.
- Use a calculator to explore patterns, then predict before pressing equals.
Ideas for the classroom
- Use a place value slider: a strip of digits that slides under a fixed decimal point.
- Link to converting metric units, which uses exactly the same skill.
- Ask students to explain in words why 0.4 × 10 = 4.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
Why is 'just add a zero' not taught?
It only works for whole numbers being multiplied. For decimals it gives wrong answers (3.5 × 10 is not 3.50), so schools teach moving digits in place value columns.
Does the decimal point move?
Many teachers describe it as the digits moving while the point stays fixed, because that matches place value. Both descriptions give the same answer.
What is the US equivalent?
Common Core 5.NBT.A.2 (Grade 5): explain patterns when multiplying a number by powers of 10, and in the placement of the decimal point.