Place value with big and small numbers
The same ten digits describe the width of an atom and the distance to the Moon. Place value is the trick that makes that possible.
Part of your national curriculum
- Number: Understand and use place value for decimals, measures and integers of any size
Lesson overview
What you'll learn in this lesson
Understand and use place value for decimals, measures and integers of any size
Key learning points
- • Columns keep growing
- • Worked example
- • Reading measures
This lesson at a glance
- 25 minutes
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Watch first
Place value with big and small numbers
From an atom to a galaxy — the same ten digits describe both.
In a nutshell
Understand and use place value for decimals, measures and integers of any size
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Columns keep growing
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Columns keep growing
Each column is ten times the one to its right: units, tens, hundreds, thousands, and so on forever. Moving left multiplies by 10; moving right divides by 10. So 4,000,000 is 4 × 1,000,000, and 0.004 is 4 ÷ 1,000.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 17
Learn
Worked example
Multiply 3.6 by 100. Each digit shifts two columns left: 3.6 × 100 = 360. Now divide 360 by 1000: each digit shifts three columns right, giving 360 ÷ 1000 = 0.36.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Reading measures
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Reading measures
A distance of 1.5 km is 1,500 m because kilo means ×1000. A mass of 250 mg is 0.25 g because milli means ÷1000. Matching the prefix to the place-value shift avoids silly errors.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 17
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Each digit shifts two ____ left: 3.6 × 100 = 360.
Challenge round
Part 15 of 17
Game · Recall cards
What is 3.6 × 100?
Card 1 of 3
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Place value with big and small numbers
3 questions, marked with the reasoning shown. No timer.
1. What is 3.6 × 100?
2. What is 250 mg in grams?
3. Which is bigger, 0.09 or 0.1?
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
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Ask LunaPart 1 of 17 · Watch & discover
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Understand and use place value for decimals, measures and integers of any size