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Year 6 Maths Length, Perimeter & Area

Convert between metric units of length - m & km

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Theory

A kilometre is \(1000\) metres. To change kilometres to metres, multiply by 1000; to change metres to kilometres, divide by 1000. This Year 6 maths page shows how to convert whole and decimal distances, such as \(2.75\) km \(= 2750\) m, and how to compare and order distances given in different units.

Kilo means one thousand, so \(1\) km \(= 1000\) m. Kilometres are used for distances between places; metres for shorter distances such as running tracks.

km to m: multiply by \(1000\) (the digits move \(3\) places left): \(2.75\) km \(= 2750\) m.

m to km: divide by \(1000\) (the digits move \(3\) places right): \(4300\) m \(= 4.3\) km; \(45\) m \(= 0.045\) km.

Useful facts: \(200\) m \(= 0.2\) km, \(100\) m \(= 0.1\) km, \(10\) m \(= 0.01\) km.

Matching kilometres and metres Two parallel number lines from 0 to 2 kilometres. The ticks line up: 0, 0.5, 1, 1.5 and 2 kilometres match 0, 500, 1000, 1500 and 2000 metres. km 0 0.5 1 1.5 2 m 0 500 1000 1500 2000
Each kilometre is \(1000\) m, so half a kilometre is \(500\) m.
Kilometres to metres machine A machine: kilometres times 1000 gives metres; a red arrow back underneath divides by 1000. km m × 1000 ÷ 1000
km \(\to\) m: \(\times 1000\). m \(\to\) km: \(\div 1000\).

Metres and kilometres:

\[ 1\text{ km} = 1000\text{ m} \]
1 km =1000 m
\[ \text{km} \times 1000 = \text{m} \]
km ×1000= m
\[ \text{m} \div 1000 = \text{km} \]
m ÷1000= km
\[ 0.5\text{ km} = 500\text{ m}, \quad 0.1\text{ km} = 100\text{ m} \]
0.5 km =500 m ,0.1 km =100 m
Three places. \(\times 1000\) and \(\div 1000\) move the digits three places: fill gaps with zeros.
Not 100. There are \(1000\) m in a kilometre, not \(100\).

How to convert

  1. km to m: multiply by \(1000\).
  2. m to km: divide by \(1000\).
  3. Check: the number of metres should be bigger than the number of kilometres.

How to compare distances

  1. Write every distance in metres.
  2. Compare or order the numbers, then write the answer in the original units.
Example 1 — km to m
How many metres are in \(6\) km?
Solution
\(6 \times 1000\)\(=\)\(6000\)
6×1000=6000

\(6000\) m.

Example 2 — m to km
Write \(9000\) m and \(4300\) m in kilometres.
Solution
\(9000 \div 1000\)\(=\)\(9\)
\(4300 \div 1000\)\(=\)\(4.3\)
9 km ,4.3 km

\(9\) km and \(4.3\) km.

Example 3 — Decimal kilometres
Convert to metres.
(i) \(0.6\) km
(ii) \(2.75\) km
Solution
\(0.6 \times 1000\)\(=\)\(600\)
\(2.75 \times 1000\)\(=\)\(2750\)
600 m ,2750 m

(i) \(600\) m
(ii) \(2750\) m

Example 4 — A short distance
Write \(45\) m in kilometres.
Solution
\(45 \div 1000\)\(=\)\(0.045\)
45÷1000=0.045

\(0.045\) km.

Example 5 — Road sign and track
(i) A sign says a town is \(18\) km away. How many metres is that?
(ii) Five laps of a \(400\) m track: how many kilometres?
Solution
\(18 \times 1000\)\(=\)\(18\,000\)
\(5 \times 400\)\(=\)\(2000\)
18000 m ,2000 m =2 km

(i) \(18\,000\) m
(ii) \(2000\) m \(= 2\) km

Example 6 — Who went further?
Ana cycled \(4.6\) km and Ben cycled \(4750\) m.
(i) Who went further?
(ii) By how many metres?
Solution
\(4.6 \times 1000\)\(=\)\(4600\)
\(4750 - 4600\)\(=\)\(150\)
4750−4600=150

(i) Ben
(ii) \(150\) m

Example 7 — Order
Order these walks from shortest to longest: \(2.1\) km, \(1950\) m, \(2015\) m.
Solution

In metres: \(2100\), \(1950\), \(2015\).

\(1950\) m, \(2015\) m, \(2.1\) km.

Example 8 — Find the mistake
Raj changed \(3400\) m to kilometres by dividing by \(100\) and wrote \(34\) km. What is right?
Solution
\(3400 \div 1000\)\(=\)\(3.4\)
3400÷1000=3.4

There are \(1000\) m in a kilometre, so divide by \(1000\): \(3.4\) km.

Common pitfalls

Dividing by 100. \(3400\) m is \(3.4\) km, not \(34\) km.
Missing zeros. \(0.045\) km is \(45\) m; \(0.45\) km is \(450\) m.
Comparing different units. \(4750\) m is more than \(4.6\) km, even though \(4.6\) looks smaller.
Multiplying the wrong way. Metres to kilometres makes the number smaller.

Frequently asked questions

How many metres are in a kilometre?

\(1000\).

How do I change km to m?

Multiply by \(1000\): \(2.75\) km \(= 2750\) m.

How do I change m to km?

Divide by \(1000\): \(4300\) m \(= 4.3\) km.

What is 200 m in kilometres?

\(0.2\) km.

How do I compare 4.6 km and 4750 m?

Change to metres: \(4600\) m is less than \(4750\) m.

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