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Year 6 Maths Mass

Convert between metric units of mass - kg & t

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Theory

A tonne (t) is \(1000\) kilograms. To change tonnes to kilograms, multiply by 1000; to change kilograms to tonnes, divide by 1000. This Year 6 maths page shows how to convert masses such as \(5\) t \(400\) kg \(= 5400\) kg \(= 5.4\) t, and how to solve problems about heavy loads.

Tonnes measure very heavy things: cars, trucks, boats, harvests. A small car has a mass of about \(1\) to \(1.5\) t.

\(1\) t \(= 1000\) kg, in the same way as \(1\) kg \(= 1000\) g.

t to kg: multiply by \(1000\). \(2.4\) t \(= 2400\) kg; \(0.09\) t \(= 90\) kg.

kg to t: divide by \(1000\). \(3600\) kg \(= 3.6\) t; \(650\) kg \(= 0.65\) t.

\(4\) t \(35\) kg means \(4000 + 35 = 4035\) kg, which is \(4.035\) t. The kilograms fill the first three decimal places.

Tonnes to kilograms machine A machine: tonnes times 1000 gives kilograms. A red arrow back underneath divides by 1000 to go from kilograms to tonnes. t kg × 1000 ÷ 1000
t \(\to\) kg: \(\times 1000\). kg \(\to\) t: \(\div 1000\).
Truck and load bar model A bar split into two parts: the empty truck, 6.5 tonnes, and the load, 3200 kilograms. The whole bar is 9700 kilograms, which is 9.7 tonnes. 9700 kg = 9.7 t truck 6.5 t load 3200 kg
Write both parts in kilograms before adding: \(6500 + 3200 = 9700\) kg.
Matching tonnes and kilograms Two parallel number lines from 0 to 1 tonne. The ticks line up: 0, 0.25, 0.5, 0.75 and 1 tonne match 0, 250, 500, 750 and 1000 kilograms. t 0 0.25 0.5 0.75 1 kg 0 250 500 750 1000
Half a tonne is \(500\) kg.

Kilograms and tonnes:

\[ 1\text{ t} = 1000\text{ kg} \]
1 t =1000 kg
\[ \text{t} \times 1000 = \text{kg} \qquad \text{kg} \div 1000 = \text{t} \]
t ×1000= kg , kg ÷1000= t
TonnesKilograms
\(0.05\) t\(50\) kg
\(0.5\) t\(500\) kg
\(2.6\) t\(2600\) kg
\(4.035\) t\(4035\) kg
Same as grams and kilograms. The step from kilograms to tonnes is \(1000\), just like grams to kilograms.
Check the decimal places. \(40\) kg is \(0.04\) t, so \(6\) t \(40\) kg is \(6.04\) t, not \(6.4\) t.

How to convert

  1. t to kg: multiply by \(1000\).
  2. kg to t: divide by \(1000\).
  3. Tonnes and kilograms together: write the tonnes in kilograms and add the kilograms.

How to solve a load problem

  1. Write every mass in kilograms.
  2. Add (or multiply for many equal items).
  3. Compare with the limit and give the answer in the unit asked.
Example 1 — t to kg
Write in kilograms.
(i) \(7\) t
(ii) \(2.4\) t
Solution
\(7 \times 1000\)\(=\)\(7000\)
\(2.4 \times 1000\)\(=\)\(2400\)
7000 kg ,2400 kg

(i) \(7000\) kg
(ii) \(2400\) kg

Example 2 — kg to t
Write in tonnes.
(i) \(9000\) kg
(ii) \(3600\) kg
(iii) \(650\) kg
Solution
\(9000 \div 1000\)\(=\)\(9\)
\(3600 \div 1000\)\(=\)\(3.6\)
\(650 \div 1000\)\(=\)\(0.65\)
9 t ,3.6 t ,0.65 t

(i) \(9\) t
(ii) \(3.6\) t
(iii) \(0.65\) t

Example 3 — Tonnes and kilograms
Write \(5\) t \(400\) kg in kilograms and in tonnes.
Solution
\(5 \times 1000 + 400\)\(=\)\(5400\)
5×1000+400=5400

\(5400\) kg, which is \(5.4\) t.

Example 4 — A small part of a tonne
How many kilograms is \(0.09\) t?
Solution
\(0.09 \times 1000\)\(=\)\(90\)
0.09×1000=90

\(90\) kg.

Example 5 — Truck and load
An empty truck has a mass of \(6.5\) t. It carries a load of \(3200\) kg. What is the total mass in tonnes?
Solution
\(6500 + 3200\)\(=\)\(9700\)
6500+3200=9700

\(9700\) kg \(= 9.7\) t (see the bar model).

Example 6 — Many sacks
Each sack of fertiliser has a mass of \(20\) kg.
(i) What is the mass of \(75\) sacks, in tonnes?
(ii) How many sacks make \(2\) t?
Solution
\(75 \times 20\)\(=\)\(1500\)
\(2000 \div 20\)\(=\)\(100\)
1500 kg =1.5 t 100 sacks

(i) \(1500\) kg \(= 1.5\) t
(ii) \(100\) sacks

Example 7 — Order
Order these boats from lightest to heaviest: \(1.3\) t, \(1250\) kg, \(0.95\) t, \(1080\) kg.
Solution

In kilograms: \(1300\), \(1250\), \(950\), \(1080\).

\(0.95\) t, \(1080\) kg, \(1250\) kg, \(1.3\) t.

Example 8 — Bridge limit
A bridge has a limit of \(12\) t. A truck of mass \(8.6\) t carries \(3750\) kg of logs.
(i) What is the total mass in tonnes?
(ii) Can it cross? By how much is it over or under?
Solution
\(8600 + 3750\)\(=\)\(12\,350\)
\(12\,350 - 12\,000\)\(=\)\(350\)
8600+3750=1235012350−12000=350

(i) \(12.35\) t
(ii) No: it is \(350\) kg over the limit.

Example 9 — Find the mistake
Kim wrote \(6\) t \(40\) kg as \(6.4\) t. What is right?
Solution
\(6 \times 1000 + 40\)\(=\)\(6040\)
6×1000+40=6040

\(40\) kg is \(0.04\) t, so the mass is \(6040\) kg \(= 6.04\) t. (\(6.4\) t would be \(6\) t \(400\) kg.)

Common pitfalls

Treating kilograms as tenths. \(6\) t \(40\) kg is \(6.04\) t, not \(6.4\) t.
Adding different units. \(6.5\) t \(+ 3200\) kg is not \(3206.5\): change to kilograms first.
Dividing by 100. \(3600\) kg is \(3.6\) t, not \(36\) t.
Comparing the numbers only. \(1080\) kg is less than \(1.3\) t.

Frequently asked questions

How many kilograms are in a tonne?

\(1000\).

How do I change tonnes to kilograms?

Multiply by \(1000\): \(2.4\) t \(= 2400\) kg.

How do I change kilograms to tonnes?

Divide by \(1000\): \(3600\) kg \(= 3.6\) t.

What is 4 t 35 kg in tonnes?

\(4.035\) t.

What is heavier, 0.95 t or 1080 kg?

\(1080\) kg, because \(0.95\) t is only \(950\) kg.

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