Right, let's pick this up — Page 281, Lesson 247

Right, let's pick this up. We've just finished a worked example that gave us an answer of 45.89 nautical miles, and now I want to talk about something that trips up a lot of students: rounding errors. Here's the reality. The conversion factors we use—like the 1.852 kilometres per nautical mile, or the 6,076 feet per nautical mile—are, in many cases, only approximate. They're rounded off for convenience. So when you're doing a scale problem, there's often more than one way to carry out the conversion. Sometimes you can solve a problem by converting both the numerator and the denominator into metric units, or alternatively, you could convert both of them into imperial units. And because those conversion factors are approximate, these two different routes can give you small differences in the answers. So what do you do when you get two slightly different answers? Look at the four options given in the question and choose the nearest one. That's the practical rule. The examiners know about this, and the answer options are designed so that the nearest one is clearly the intended answer. Now, let's move on to a concept that causes a huge amount of confusion: large scale versus small scale. I want to clear this up once and for all. Think about a UK Ordnance Survey map. That's a classic example of a large scale chart, and it has a scale of 1:50,000. What does that mean? It means one unit on the chart represents 50,000 of the same units on the ground. So two centimetres on this chart represents one kilometre on the Earth. Now, the key characteristics: this chart does not cover much area, but there is lots of detail. That's the essence of a LARGE scale chart—lots of detail. Now contrast that with a world atlas. That's an example of a small scale chart. It covers a lot of area, but there is not much detail. So the memory aid is simple: LARGE SCALE means LOTS OF DETAIL, and SMALL SCALE means LOTS OF AREA. But here's where the confusion creeps in. The Representative Fraction—that's the RF, the 1 over something ratio—is actually in the right sense. A SMALL scale gives a SMALLER RF. A LARGE scale gives a LARGER RF. Let me show you with the two examples we just mentioned. Take the 1/50,000 Ordnance Survey chart. If you express that as a decimal, you get 0.00002. Now take the 1/5,000,000 small scale chart. As a decimal, that's 0.0000002. You can see that 0.00002 is a LARGER number than 0.0000002. So the Representative Fractions are in the right sense—large scale, larger RF; small scale, smaller RF. So where does the confusion come from? It's because the denominators are easier to handle, and that's how we usually refer to charts in conversation. We call the first chart a "fifty thousand" in conversation. We call the second one a "five million". We do not refer to them as a "0.00002" or a "0.0000002". But the logic of 'large' or 'small' is correct. So let me give you the two rules to remember. LARGE SCALE means SMALLER DENOMINATOR. SMALL SCALE means LARGER DENOMINATOR. That's the key takeaway. The denominator is the bottom number of the fraction. A large scale chart like 1/50,000 has a smaller denominator than a small scale chart like 1/5,000,000. It sounds backwards, but once you see the decimal values, it makes perfect sense.