The Navigation Computer - Slide Rule Face — Page 71, Lesson 81

I want to walk you through how multiplication and division work on the Navigation Computer's slide rule face. This is the core of how we'll solve speed-distance-time problems and fuel calculations later, so let's get the principle solid right now. First, look at the scale itself. From Figure 4.12, you can see that there is no number smaller than 10 or larger than 99.9 printed on the scale. That means the scale only shows numbers between 10 and 99.9 — nothing below 10, nothing above 99.9. So how do we handle a number like 11.5 or 3050? We have to mentally insert the decimal point ourselves. For instance, the number 12 on the scale can be used to represent 0.12, 12, 120, 1200, or any other power-of-ten variation. We put the decimal point in after we finish the Navigation Computer operation. This means you have to carry out a rough calculation in your head first, to know what order of magnitude your solution will be. 'Order of magnitude' just means whether the answer is roughly 2.5, 25, 250, or 2500 — you need to know which one is correct before you read the scale. Let me show you with an example. Suppose you have to multiply 11.5 by 2.54. First, do the approximate calculation in your head. 11.5 is approximately 10, and 2.54 is approximately 2½. So 10 times 2½ is 25. The answer will be approximately 25. It will not be 2½ or 250 — that's the order of magnitude we've established. Now we know the order of magnitude, we can use the slide rule. Against 11.5 on the outer scale, you line up 10 on the inner scale. Wait — why 10? Because the inner scale's '10' actually represents 1.0 for this operation. Remember, the scale has no number smaller than 10, so we use 10 to stand for 1.0 when we need it. So you align 11.5 on the outer scale with 10 (representing 1.0) on the inner scale, as shown in Figure 4.13. Now find 2.54 on the inner scale. On the scale, 2.54 is shown as 25.4 — again, you mentally place the decimal. Align the cursor over that 25.4 on the inner scale, as in Figure 4.14. Then read off the answer on the outer scale, which gives you 29.2. Now check: is the answer 2.92, 29.2, or 292? We know from our rough calculation that the answer is about 25. So 29.2 is the correct order of magnitude. The decimal goes after the 29, giving 29.2. Now let's look at division. Divide 3050 by 3.28. Again, start with the rough calculation. 3050 is approximately 3000, and 3.28 is approximately 3. So 3000 divided by 3 is 1000. The answer will be just under 1000 — about nine hundred and something. Find 3050 on the outer scale and align the cursor over it. Now find 3.28 on the inner scale — that's shown as 32.8 on the scale — and align it with the cursor. That sets up the division, as shown in Figure 4.15. Now here's the key step for division: find 10 on the inner scale — again, that 10 represents 1.0 — and read off against the outer scale, as in Figure 4.16. The initial answer you read is 93.0 on the outer scale. Is that the right order of magnitude? We know from our rough calculation that it should be about 900, so the correct answer must be 930. The scale gave us 93.0, but we mentally place the decimal to get 930. So the pattern is always the same: rough calculation first to know the order of magnitude, then set up the scales, read the raw number, then apply the decimal point based on your rough estimate. That's how we avoid reading 29.2 when we mean 292, or 93.0 when we mean 930.