Convert measurements using decimals

What you will learn

• Convert measurements using decimals

Models used: number sentences, stories, tables.

Before you start

• Multiply and divide three-place decimals by powers and multiples of 10

A new unit for the same amount

One m contains 100 cm. We can measure the same amount using either unit.

1. The complete bar is the whole. Each labelled section is one part of it.

   One m contains 100 cm. We can measure the same amount using either unit.

   The amount does not grow when we change its name. Smaller units simply need a bigger count.

   100

   1001 m = 100 cm

2. The complete bar is the whole. Each labelled section is one part of it.

   Two m contain two groups of 100 cm.

   2 × 100 = 200 cm

   First convert the larger-unit part by multiplying by 100.

   200

   1001 m1001 m

3. The complete bar is the whole. Each labelled section is one part of it.

   Add another 50 cm. The complete amount is 250 cm.

   200 + 50 = 250 cm

   The last part is already in small units. Add it after converting the larger units.

   250

   1001 m1001 m5050 cm
   Why do we need more small units than large units?

   Each small unit measures less, so more of them are needed to describe the same amount.

Worked example: A new example, together

Convert 3900 ml to litres.

1. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   Write the relationship between the two units and track complete units plus any remainder.

   Changing units changes the number we count, while the measured amount stays the same.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

2. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   1 litres = 1000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

   Convert 3900 ml to litres.

   3.9 litres

3. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   1 litres = 1000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

4. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   3 litres = 3000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

5. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   3000 + 900 = 3900 ml; this is 3.9 litres.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

6. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   Check the result against the question we started with.

   3900 ÷ 1000 = 3.9 litres.

   We found 3.9 litres. Changing units changes the number we count, while the measured amount stays the same.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   3 litres	3000 ml

Common mistakes to discuss

• Using one multiplier for every unit. The pairs differ: 100 cm make a metre but 1000 g make a kilogram. So 1 kg 250 g is 1.25 kg, while 3 m 45 cm is 3.45 m.

Check your understanding

• Convert measurements using decimals
• justify a conversion while preserving the measured quantity
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.