Mass and Capacity: Conversions and Applications

In this lesson you will:

• Convert mass between grams, kilograms, and tonnes
• Convert capacity between millilitres, centilitres, decilitres, and litres
• Solve real-life problems using the right ladder and the right direction

The Trader's Two Opening Questions

A market trader has:

• 2.5 tonnes of maize flour to pack into 500 g bags
• 3.5 litres of cooking oil to pour into 25 ml bottles

How many bags? How many bottles? What do you need to know first?

×1000 Recall: Check Your Digit-Shift Tools

Before we build the ladder, check your place-value tools.

Think of it as a digit shift: multiply by 1000 moves every digit three places to the left.

The Mass Ladder: g, kg, Tonne

• 1 kg = 1000 g — going down (g is smaller): ×1000
• 1 tonne = 1000 kg — going down (kg is smaller): ×1000
• Going up to a larger unit: ÷1000 at each rung
• Each jump is exactly ×1000 — not ×10, not ×100

Which Direction? Smaller or Larger?

Rule: moving to a smaller unit → the number gets bigger (multiply)

Rule: moving to a larger unit → the number gets smaller (divide)

Sanity check: 4200 g is a few kilograms — a small number, not millions.

If your answer feels the wrong size, you went the wrong direction.

Mass Ladder: Four Worked Examples

Down the ladder (×1000):

Up the ladder (÷1000):

Predict the Direction Before You Compute

Before computing: is your answer going to be bigger or smaller than 4200?

• A. Bigger — I multiply by 1000
• B. Smaller — I divide by 1000

Commit to A or B. Then check your answer against the sanity rule.

Practice: Convert These Mass Units

Convert the following. Choose your direction first.

Pause, work each one out, then advance for the answers.

Does Capacity Use ×1000 Per Step?

The mass ladder steps by ×1000 each rung.

Predict before the next slide:

Does the capacity ladder also use ×1000 per step?

• Yes — all metric ladders step by ×1000
• No — the capacity ladder is different

Commit to Yes or No now.

The Capacity Ladder: ml, cl, dl, Litre

• 10 ml = 1 cl — one rung up: ×10
• 10 cl = 1 dl — one rung up: ×10
• 10 dl = 1 litre — one rung up: ×10
• Total: 1000 ml = 1 litre (three ×10 steps, not one ×1000 jump)

Capacity Steps Are ×10, Not ×1000

Common error: applying the mass rule to capacity.

• ✗ Wrong:
• ✓ Right:

Bridge: 1 ml = 1 cm³

From measurement-03 you already know:

This connects to the capacity ladder:

Volume and capacity are the same measurement in different units.

Capacity Ladder: Four Worked Examples

Down (×10 per rung):

• 2.5 l × 10 × 10 × 10 = 2500 ml
• 2 dl × 10 = 20 cl × 10 = 200 ml

Up (÷10 per rung):

• 350 ml ÷ 10 = 35 cl
• 50 cl ÷ 10 = 5 dl

Practice: Convert These Capacity Units

Convert the following. Use ×10 or ÷10 per rung.

Work through each one before advancing.

Now We Can Solve the Trader's Problem

Two ladders, two questions:

Solve Real-Life Problems: The Routine

Three steps every time:

1. Decide the target unit — what unit does the final question use?
2. Convert all quantities to that unit
3. Compute — add, subtract, divide, or compare

Never add or compare quantities in different units.

Trader Problem 1: Flour Bags

Target unit: grams (the bag size is in grams)

How many 500 g bags?

Trader Problem 2: Oil Bottles

Target unit: millilitres (the bottle size is in millilitres)

How many 25 ml bottles?

Try These Without a Scaffold

No hints — choose the unit, then convert.

1. A lorry carries 15 sacks of 50 kg each. Total load in tonnes?
2. A recipe uses 250 ml per batch × 6 batches. Total in litres?

Write your target unit before calculating.

From Two Ladders to One Chain

You have used mass and capacity separately. Real problems chain them.

• Volume (cm³) → Capacity (litres) via:
• Capacity (litres) → Mass (kg) via:

Three strands — one connected chain.

Chain: Volume to Capacity to Mass

Decompose an L-Shaped Tank Step by Step

Split into two cuboids:

• Part A: 40 × 30 × 20 cm → 24 000 cm³
• Part B: 20 × 30 × 20 cm → 12 000 cm³
• Total: 36 000 cm³ → 36 litres → 36 kg of water

Two Questions Close Every Conversion Problem

✓ Mass: g → kg → tonne: ×1000 per rung
✓ Capacity: ml → cl → dl → l: ×10 per rung
✓ Down = multiply. Up = divide.
Capacity steps are ×10, not ×1000.
Convert to a common unit before adding.