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Ratio, proportion & rates of change · Compound units & rates

Chapter 1 · 4

The idea

Converting compound units and rates of flow

Why converting a compound unit means converting both of its parts, where the ÷3.6 between km/h and m/s comes from, why g/cm³ to kg/m³ is ×1000, and how rates of flow work.

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Ratio, proportion & rates of change · Compound units & rates

Converting compound units and rates of flow

Why converting a compound unit means converting both of its parts, where the ÷3.6 between km/h and m/s comes from, why g/cm³ to kg/m³ is ×1000, and how rates of flow work.

Why it works

Convert BOTH parts

A compound unit like km/h is built from two simple units — so converting it means converting both parts, top and bottom. Convert only one and the answer is silently wrong: the number looks plausible, the units claim something else entirely. Every conversion in this lesson is the same three-step recipe — write the rate as a fraction of units, convert top and bottom separately, recombine.

km/h to m/s, from first principles

Take 54 km/h. Convert the top: 5454 km =54×1000=54 000= 54 \times 1000 = 54\,000 m. Convert the bottom: 1 hour =3600= 3600 s. So

54 km/h=54 000 m3600 s=15 m/s54 \text{ km/h} = \frac{54\,000 \text{ m}}{3600 \text{ s}} = 15 \text{ m/s}

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