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Concept 2 of 9

The Number Line Dance: The Metric Decimal Slide

1

Today's big idea

Metric units sit ten apart, so converting is just sliding the decimal point.

Each step is x10, so m to cm is 2 steps and m to mm is 3 steps.

2

How it works

👀 What's going on?

Metric units are built so that every step between them is a group of ten. That single fact turns converting into sliding a decimal point, with almost no working out at all.

💡 Here's the trick

The metric staircase — each step is ×10bigger unit: slide LEFT, ÷10 each stepkmhmdammdmcmmmsmaller unit: slide RIGHT, ×10 each step1 m = 100 cm (2 steps)1 m = 1000 mm (3 steps)count the steps, slide that many places

Look at the staircase above. Every single step is worth ten, and the units you meet most are km, m, cm and mm. They are not all neighbours: from m down to cm is two steps, and from m down to mm is three. Count the steps between your two units, then slide the decimal point that many places. Towards a bigger unit you slide left and the number shrinks. Towards a smaller unit you slide right and it grows.

🪄 How to do it

  1. 1.Count the steps between your two units on the staircase above.
  2. 2.Going to a bigger unit, slide the point left. Going to a smaller one, slide it right.
  3. 3.Move one place for every step you counted.

✍️ Try it

Change 250 cm into metres, change 3 m into centimetres, then change 2 m into millimetres. How many places does each one move?

Going cm to m is 2 steps up, so slide 2 places left and 250 becomes 2.5 m. m to cm is 2 steps down, so slide 2 places right and 3 becomes 300 cm. m to mm is 3 steps down, so slide 3 places right and 2 becomes 2,000 mm. The step count sets how far you slide.

⚠️ Watch out

You might be thinking the point always slides the way you read, to the right. Going to a bigger unit slides it left instead. Sense-check the size: 4,500 m cannot possibly become 4,500,000 km, because a kilometre is longer than a metre.

🌟 Why this matters

Race distances, bottle labels and map scales all switch between metric units, and this trick does the switch in your head with nothing written down.
Exam tip: Metric conversions become the fastest marks on the page once the sliding direction is automatic.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Convert 3.2 km to m.”

  1. 1

    Count the steps

    km → m is 3 steps DOWN the metric scale.

  2. 2

    Slide the decimal RIGHT

    Down the scale means slide the decimal point right — 3 places.

  3. 3

    Apply the slide

    3.2 → 32 → 320 → 3,200

  4. 4

    Done ✓

    3.2 km = 3,200 m

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

Tap a FROM unit, then a TO unit. Count the jumps — slide the decimal!

FROM unit (tap to select):

TO unit (tap to select):

5

Quick check

✅ VERIFICATION

Change 7,200 m into kilometres.

⚡ Finish the activity above first to answer.

Keep going!

Up next: The Potion Mixer

Mix and split amounts from teaspoons to litres.

Concept 3 of 9 →