First, let's talk about rounding errors — Page 281, Lesson 247

I want to walk you through a couple of important concepts that build on the conversion work we've been doing. First, let's talk about rounding errors. The conversion factors we use—for example, turning nautical miles into kilometres or statute miles—are often only approximate values. Because of that, there's usually more than one correct way to carry out a conversion. Sometimes you might solve a scale or distance problem by converting both the numerator and denominator into metric units; other times you might convert both into imperial units. These different routes can produce small differences in the final answer. So when you're faced with a multiple-choice question, look at the four options given and choose the nearest one. Don't expect an exact match down to the last decimal. Now, let's move to a topic that causes a lot of confusion: the difference between large scale and small scale on a chart. A UK Ordnance Survey Map is a classic example of a large scale chart. Its scale is 1:50 000. That means two centimetres on this chart represents one kilometre on the Earth's surface. Because the scale is large, the chart doesn't cover much area—but it shows lots of detail. That's the key: large scale means lots of detail. On the other hand, a world atlas is an example of a small scale chart. It covers a huge area, but there isn't much detail. So small scale means lots of area. Here's where the confusion often creeps in. The Representative Fraction, or RF, is actually in the right sense. A small scale chart gives you a smaller RF. A large scale chart gives you a larger RF. Let me show you with two examples. Take a large scale chart like the 1/50 000 Ordnance Survey map. Its Representative Fraction expressed as a decimal is 0.00002. Now take a small scale chart like a 1/5 000 000 world chart. Its RF as a decimal is 0.0000002. You can see that 0.00002 is a larger number than 0.0000002. So the Representative Fractions are indeed in the right sense: large scale gives a larger RF, small scale gives a smaller RF. The confusion happens because we usually refer to charts by their denominators—those are easier to handle in conversation. We call the first chart a "fifty thousand" and the second one a "five million." We don't walk around saying "zero point zero zero zero zero two" or "zero point zero zero zero zero zero zero two." But the logic of 'large' or 'small' is correct when you think about the RF itself. So here's the rule to remember: Large scale means a smaller denominator. Small scale means a larger denominator. That's the opposite of what you might first think, but it follows directly from the Representative Fraction. Large scale—smaller denominator. Small scale—larger denominator. Keep that straight, and you'll avoid the common pitfall.