Concept 1 of 7
Length: Decimals on the Metric Ladder
Today's big idea
Down the ladder multiply by 10, 100 or 1,000; up the ladder divide.
Every step is a power of 10, so converting is a decimal slide, not a sum.
How it works
👀 What's going on?
How tall are you in mm? Nobody answers that way, and nobody gives the distance to the next town in cm. Same idea, different rungs of one ladder.
💡 Here's the trick
Look at the ladder above. Every rung is a length unit, and every step is worth 10, 100 or 1000. Step down to a smaller unit and you multiply. Step up to a bigger unit and you divide.
🪄 How to do it
- 1.Find both units on the ladder above.
- 2.Count the steps between them to get the factor.
- 3.Multiply going down, divide going up.
✍️ Try it
Change 7 km into m. Then: change 830 cm into m.
From km to m is one step down, so 7 × 1000 = 7,000 m. From cm to m is one step up, so 830 ÷ 100 = 8.3 m.
⚠️ Watch out
You might be thinking every step on the ladder is worth 10. It is not. Notice that m to km is a jump of 1000, so 500 m is 0.5 km and never 50 km.
🌟 Why this matters
Bus routes come in km, a school desk comes in cm, and a pencil lead comes in mm. Sliding between them lets you compare any two lengths at a glance.
Exam tip: Put every length into the smallest unit first, then compare plain whole numbers.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Convert 4.5 km to metres.”
- 1
Going BIG → SMALL
km → m is going DOWN the ladder. 📏
- 2
Pick the factor
1 km = 1,000 m, so multiply by 1,000.
- 3
Slide the point 3 places RIGHT
4.5 → 4,500
- 4
Answer ✓
4.5 km = 4,500 m
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Step the marker from km to m. Every rung is ×10 (or ÷10 going up).
LENGTH LADDER · ROUND 1 OF 3
Convert 3 km to m
Quick check
✅ VERIFICATION
How many millimetres are in 12 cm?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Mass
mg, g, kg, t — each jump ×1000. 6,200 g = 6.2 kg.