Concentration required

Well, I learnt a lot about how maths is used in healthcare contexts from working on the new book. Here's an interesting something I didn't know before.

When you see the concentration of a chemical given as a percentage, such as the commonly-used sodium chloride 0.9%, what exactly does this 0.9% mean?

Well, when a solid (like sodium chloride) is dissolved in a liquid (water) then the concentration of the solution is given as weight by volume (w/v). So, the 0.9% is understood to mean 0.9 grams in 100 millilitres of solution.

Similarly a solution of dextrose 5% has 5 grams of dextrose dissolved in 100 millilitres of the solution.

Extra 20% is not an extra 20%!

We are into the summer sales and in some shops we begin to see reduced items with a blue ticket announcing 'an extra 20% off this item'. I saw one today: an article already reduced to '50% off', with an 'extra 20% off'. What they don't always make clear is that the 'extra 20% off' is 20% of the reduced price. So, it is not really an extra 20% off – in fact it is always less than this.

For example, if an article costing £100 has 50% off then it now costs £50. Most people I talk to think the 'extra 20%' would be an additional £20 reduction. But they are being misled into thinking this. It is only 20% of the reduced price; that's 20% of £50 in this case, a mere £10.

So, 50% off with an additional 20% off is only 60% off in total!

Here's an interesting question. If they reduced the price of something by 10% every day – so every day after the first 10% reduction there is an 'extra 10% off' – assuming no-one buys it, how many days would it take before it costs nothing at all? I'll give the solution some time next week.