The answer is, with great difficulty. Instead of calculating with pencil and paper, they would have used an abacus to actually do the calculations, and then written the answer in Roman numerals. Division would have been even harder - involving breaking the calculation into a number of operations like those we now use in long division.
You might wonder why they didn't develop a positional number system like ours: the answer is probably because they didn't have a symbol for 'zero' (try doing maths without it) which was introduced later, by the Arabs.
Q Where does the word "photon" come from?
The term comes from the Greek word phos or photos, meaning light. But the word photon wasn't used until 1926. Before that a "particle" of light was called a light quantum.
Q Why don't lightning and thunder occur at exactly the same time?
Actually, they do: thunder and lightning always occur together in a storm. But most people aren't present at the point where the lightning hits. Instead, you usually witness the event some distance away. The light from the lightning travels much faster than the sound from the thunder, so the light reaches you almost instantaneously. But it takes about five seconds for sound to travel one mile. By counting the number of seconds between the lightning flash and the thunder, you can calculate how far away the storm is.
Q What's the ocean floor made of, and how thick is it?
The crust beneath the ocean differs from the crust beneath the land in several ways: it is thinner, denser, younger and made in different ways. Both have rocks made up of the same minerals, just in slightly different proportions. The crust has silicon, aluminium, iron, magnesium, calcium, sodium and potassium oxides in it - just like any other rock. However, the oceanic crust is only about four miles thick.
Q When you defrost something in a plastic container in a microwave, you often end up with a collapsed container - as if something had sucked the sides in. Why?
As you defrost things, the water on the surface escapes into the air in the container. A lot of this water will escape as superheated steam from the container, through the tiniest pores in the seal of the lid. But because these containers are designed to keep food fresh by keeping out bacteria, no air can get back in to fill the space left by the departing water. This means the air pressure inside the container is less than that outside, so the sides of the container cave inwards.
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