The C and D scales each look like a single stretched out ruler, reading from left to right. These are called “single decade” scales. The A and B scales are “double decade” scales. Each one has two smaller stretched rulers stacked end-to-end. The K scale is a triple decade scale, or three stretched rulers stacked end-to-end. Not all models have this. The C| and D| scales are the same as the C and D scales, but read right to left. These are often printed in red. Not all models have these. Note that slide rules vary, so the scales marked “C” and “D” on your slide rule may not be the same as those described here. One some slide rules the scales used for multiplication are marked “A” and “B” and are on the top. Whatever the designating letter, these scales often have the Pi symbol marked at the suitable place and are almost always the two scales opposing each other on the slides, either the upper or lower gap. It is suggested you try a few simple multiplication problems to verify that you are using the correct scale as described in the article. If “2x4” doesn’t come to “8”, try the scales on the other side of the slide rule instead.
The primary numbers on the scale begin with 1 on the extreme left edge, extend up to 9, then end with another 1 on the far right edge. These are usually all labeled. The secondary divisions, marked by the second-tallest vertical lines, divide each primary number by 0. 1. Don’t be confused if these are labeled “1, 2, 3;” remember they actually represent “1. 1, 1. 2, 1. 3” and so on. There are usually smaller divisions, typically representing increments of 0. 02. Pay close attention, since these may disappear on the high end of the scale, where numbers get closer together.
For instance, if the answer falls between the 6. 51 and 6. 52 marks, write down whichever value it’s closer to. If you can’t tell, write 6. 515.
In Example 1 throughout this section, we’ll calculate 260 x 0. 3. In Example 2, we’ll calculate 410 x 9. This ends up being a little more complicated than Example 1, so you might want to follow Example 1 first.
Example 1: to calculate 260 x 0. 3 on a slide rule, start with 2. 6 x 3 instead. Example 2: to calculate 410 x 9, start with 4. 1 x 9 instead.
Example 1: slide the C scale so the left index is in line with the 2. 6 on the D scale. Example 2: slide the C scale so the left index is in line with the 4. 1 on the D scale.
Example 1: slide the cursor so it points to 3 on the C scale. At this position it should also point to 7. 8 on the D scale, or extremely close to it. Skip ahead to the estimation step. Example 2: try to slide the cursor so it points to the 9 on the C scale. On most slide rules, this will not be possible, or the cursor will be pointing to empty air off the end of the D scale. See the next step for how to fix this.
Example 2: slide the C scale so the 1 on the far right lines up with the 9 on the D scale. Slide the cursor to 4. 1 on the C scale. The cursor is pointing to the D scale in between 3. 68 and 3. 7, so the answer must be about 3. 69.
Example 1: Our original problem was 260 x 0. 3, and the slide rule gave us an answer of 7. 8. Round the original problem to convenient numbers and solve it in your head: 250 x 0. 5 = 125. This is much closer to 78 than it is to 780 or 7. 8, so the answer is 78. Example 2: Our original problem was 410 x 9, and we read an answer of 3. 69 on the slide rule. Estimate the original problem as 400 x 10 = 4,000. The closest we can get to that by moving the decimal point is 3,690, so that must be the actual answer.
For example, to solve 6. 12, slide the cursor to 6. 1 on the D scale. The corresponding A value is about 3. 75. Estimate 6. 12 to 6 x 6 = 36. Position the decimal point to get an answer near this value: 37. 5. Note that the exact answer is 37. 21. The slide rule answer is off by less than 1%, easily accurate enough for most real-world circumstances.
For example, to solve 1303, slide the cursor to 1. 3 on the D value. The corresponding K value is 2. 2. Since 1003 = 1 x 106, and 2003 = 8 x 106, we know the answer must be somewhere between them. The answer must be 2. 2 x 106, or 2,200,000.
Example 3: to solve √(390), write it as √(3. 9 x 102). Example 4: to solve √(7100), write it as √(7. 1 x 103).
If the exponent in your scientific notation is even (such as 2 in Example 3), use the left side of the A scale (the “first decade”). If the exponent in your scientific notation is odd, (such as 3 in Example 4), use the right side of the A scale (the “second decade”).
Example 3: To find √(3. 9 x 102), slide the cursor to 3. 9 on the left A scale. (Use the left scale because the exponent is even, as described above. ) Example 4: To find √(7. 1 x 103), slide the cursor to 7. 1 on the right A scale. (Use the right scale because the exponent is odd. )
Example 3: The corresponding D value at A=3. 9 is about 1. 975. The original number in scientific notation had 102. 2 is already even, so just divide by 2 to get 1. The final answer is 1. 975 x 101 = 19. 75. Example 4: The corresponding D value at A=7. 1 is about 8. 45. The original number in scientific notation had 103, so round the 3 down to the nearest even number, 2, then divide by 2 to get 1. The final answer is 8. 45 x 101 = 84. 5.
Example 5: To find the cube root of 74,000, first count the number of digits (5), divide by 3 and find the remainder (1 remainder 2). Since the remainder is 2, use the second scale. (Alternatively, count the scales five times: 1–2–3–1–2. ) Slide the cursor to 7. 4 on the second K scale. The corresponding D value is approximately 4. 2. Since 103 is smaller than 74,000, but 1003 is larger than 74,000, the answer must be in between 10 and 100. Move the decimal point to make 42.
