Concept 2 of 7
Mass: Milligrams to Tonnes, in Decimals
Today's big idea
Mass climbs in jumps of 1,000: mg to g to kg to tonne.
Grams to kilograms is one jump of a thousand, not three jumps of ten.
How it works
👀 What's going on?
Would you weigh a grain of rice and a loaded truck in the same unit? Nobody does. That is why mass gets a ladder of units of its own.
💡 Here's the trick
Look at the balance above. One pan holds 1 kg, the other holds 1,000 g, and they sit level. Mass climbs in jumps of 1000: mg to g, g to kg, kg to tonne.
🪄 How to do it
- 1.Spot the two units on the balance above.
- 2.Each jump between them is worth 1000.
- 3.Multiply going down, divide going up.
✍️ Try it
Change 9 kg into g. Then: change 6,200 g into kg.
From kg to g is one jump down, so 9 × 1000 = 9,000 g. From g to kg is one jump up, so 6,200 ÷ 1000 = 6.2 kg.
⚠️ Watch out
You might be thinking a bigger number always means a heavier thing. It does not. 900 g is lighter than 1.2 kg, because 1.2 kg is really 1,200 g.
🌟 Why this matters
Recipes ask for g, luggage rules are set in kg, and a lorry load is counted in tonnes. Reading a label and swapping units stops you buying ten times too much.
Exam tip: Rewrite every mass in grams before you order them or add them up.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Convert 3.5 kg to grams.”
- 1
Direction check
kg → g is DOWN the ladder. ⚖️
- 2
Pick the factor
1 kg = 1,000 g.
- 3
Multiply
3.5 × 1,000 = 3,500
- 4
Answer ✓
3.5 kg = 3,500 g
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Step the marker from kg to g. Every rung is ×1000 (or ÷1000 going up).
MASS LADDER · ROUND 1 OF 3
Convert 4 kg to g
Quick check
✅ VERIFICATION
How many milligrams are in 3 g?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Capacity
1 L = 1000 mL, and 1 mL of water ≈ 1 g.