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Year 6 Maths Length, Perimeter & Area

Convert between metric units of length - Mixed conversions

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Theory

The four length units are linked: \(1\) km \(= 1000\) m, \(1\) m \(= 100\) cm, \(1\) cm \(= 10\) mm. A length such as \(5\) m \(72\) cm can be written in one unit: \(572\) cm or \(5.72\) m. This Year 6 maths page shows how to convert mixed lengths, how to convert across two steps (such as km to cm), and how to compare, order and add lengths by using a common unit.

A mixed length uses two units, such as \(5\) m \(72\) cm. In centimetres it is \(5 \times 100 + 72 = 572\) cm; in metres it is \(5.72\) m.

Watch for small parts: \(4\) m \(6\) cm is \(406\) cm, or \(4.06\) m. The \(6\) cm is \(6\) hundredths of a metre.

Two-step conversions go through the middle unit: \(3\) km \(= 3000\) m \(= 300\,000\) cm.

To add or compare lengths, choose one common unit that makes the numbers easy, usually the smallest unit in the list.

Length unit ladder Boxes from top to bottom: km, m, cm, mm. Blue arrows going down are labelled times 1000, times 100 and times 10. Red arrows going up are labelled divide by 1000, divide by 100 and divide by 10. km × 1000 ÷ 1000 m × 100 ÷ 100 cm × 10 ÷ 10 mm
Going down the ladder (to a smaller unit): multiply. Going up: divide.
Matching metres, centimetres and millimetres Three parallel number lines from 0 to 4 metres. The ticks line up: 1 m matches 100 cm and 1000 mm, 2 m matches 200 cm and 2000 mm, and so on. m 0 1 2 3 4 cm 0 100 200 300 400 mm 0 1000 2000 3000 4000
\(1\) m \(= 100\) cm \(= 1000\) mm.

The length chain:

\[ 1\text{ km} = 1000\text{ m} = 100\,000\text{ cm} \]
1 km =1000 m =100000 cm
\[ 1\text{ m} = 100\text{ cm} = 1000\text{ mm} \]
1 m =100 cm =1000 mm
\[ 5\text{ m } 72\text{ cm} = 572\text{ cm} = 5.72\text{ m} \]
5 m 72 cm =572 cm =5.72 m
Two places for centimetres. In metres, centimetres take two decimal places: \(4\) m \(6\) cm \(= 4.06\) m.
Pick the smallest unit. When adding or ordering, change everything to the smallest unit in the list.

Mixed length to one unit

  1. Change the larger part to the smaller unit.
  2. Add the smaller part.

Two-step conversion

  1. Convert to the middle unit first.
  2. Then convert again to the unit you need.

Ordering or adding

  1. Choose a common unit.
  2. Convert every length, then order or add.
Example 1 — Mixed to centimetres
Write each in centimetres.
(i) \(5\) m \(72\) cm
(ii) \(4\) m \(6\) cm
Solution
\(5 \times 100 + 72\)\(=\)\(572\)
\(4 \times 100 + 6\)\(=\)\(406\)
572 cm ,406 cm

(i) \(572\) cm
(ii) \(406\) cm

Example 2 — To metres
Write each in metres.
(i) \(3850\) mm
(ii) \(6\) m \(9\) cm
Solution
\(3850 \div 1000\)\(=\)\(3.85\)
3.85 m ,6.09 m

(i) \(3.85\) m
(ii) \(6.09\) m (\(9\) cm is \(0.09\) m)

Example 3 — Mixed to millimetres
Write \(2\) m \(7\) cm in millimetres.
Solution
\(2 \times 1000 + 7 \times 10\)\(=\)\(2070\)
2000+70=2070

\(2070\) mm.

Example 4 — Two steps
How many centimetres are in \(3\) km?
Solution
\(3 \times 1000\)\(=\)\(3000\)
\(3000 \times 100\)\(=\)\(300\,000\)
3 km =3000 m =300000 cm

\(300\,000\) cm.

Example 5 — Two steps with a mixed length
How many centimetres are in \(1\) km \(400\) m?
Solution
\(1000 + 400\)\(=\)\(1400\)
\(1400 \times 100\)\(=\)\(140\,000\)
1400 m =140000 cm

\(140\,000\) cm.

Example 6 — Add in a common unit
Add \(1.4\) m and \(85\) cm. Give the answer in centimetres.
Solution
\(1.4 \times 100\)\(=\)\(140\)
\(140 + 85\)\(=\)\(225\)
140+85=225

\(225\) cm (or \(2.25\) m).

Example 7 — Order
Order from shortest to longest: \(1.6\) m, \(1450\) mm, \(0.002\) km, \(175\) cm.
Solution

In millimetres: \(1600\), \(1450\), \(2000\), \(1750\).

\(1450\) mm, \(1.6\) m, \(175\) cm, \(0.002\) km.

Example 8 — Find the mistake
Ella wrote \(4\) m \(25\) cm as \(4.25\) cm. What should it be?
Solution

\(4.25\) is the length in metres. In centimetres it is \(4 \times 100 + 25 = 425\) cm.

Common pitfalls

Writing 4 m 6 cm as 4.6 m. \(6\) cm is \(0.06\) m, so it is \(4.06\) m.
Mixing the unit names. \(4.25\) m is \(425\) cm, not \(4.25\) cm.
Skipping a step. km to cm needs \(\times 1000\) and then \(\times 100\).
Ordering by the numbers only. Change to one unit first: 0.002 km is the longest in the list.

Frequently asked questions

How do I write 5 m 72 cm in centimetres?

\(5 \times 100 + 72 = 572\) cm.

How do I write 6 m 9 cm in metres?

\(6.09\) m, because \(9\) cm is \(0.09\) m.

How many centimetres are in a kilometre?

\(100\,000\) (\(1000\) m \(\times 100\)).

Which unit should I use to add lengths?

Usually the smallest unit in the question, so there are no decimals.

How do I order 1.6 m, 1450 mm and 175 cm?

Change them all to millimetres: 1600, 1450, 1750.

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