Here is a builder's measurement: a wall is 4.7 metres long. The builder needs to write that same length in centimetres for the plan. How many centimetres is 4.7 m? Have a quick estimate before we work it out together.

Before we use the ladder, look at what happens to the digits. To change 4.7 m into centimetres, there are 100 centimetres in every metre, so we multiply by 100. Each digit slides two columns to the left. The decimal point does not move, the digits do.

So 4.7 m becomes 470 cm. The number got bigger because a centimetre is smaller than a metre, so it takes more of them to make the same length.

The interactive shows a unit ladder converting the same length between millimetres, centimetres, metres and kilometres. Notice which way each length sits along the ladder, and how the number changes as the unit changes. Look out for where the decimal point appears.

Today we work through this conversion together on the ladder: 1.5 km all the way down to millimetres. The ladder is live, so we tap one rung at a time and say the factor out loud before the digits step across: ×1000 from km to m, ×100 from m to cm, then ×10 from cm to mm.

Today we hit these conversions on the ladder: 50 mm to cm, 4 cm to mm, 6 m to cm, 2.5 km to m, then the big chain, 3 km all the way down to millimetres. The chain takes three steps in a row, ×1000 from km to m, then ×100 from m to cm, then ×10 from cm to mm, so we'll say each step aloud before we check it.

What we did today

• Converted between mm, cm, m and km using ×10, ×100 and ×1000
• Saw the digits slide left for smaller units and right for bigger units, with the decimal point staying put
• Chained conversions one step at a time, all the way from km down to mm, with a different factor at each rung