Slide rules are good for only around 3 significant digits, just a little more than most people’s mental math for multiplication. However, slide rules include s

Slide rules are good for only around 3 significant digits, just a little more than most people’s mental math for multiplication. However, slide rules include scales for squares, cubes, trig, exponential, log functions and others. All of these are inscribed as positions on logarithmic scales. In this manner, two scales can positioned to calculate products and quotients. The scales, being logarithmic, are very compressed on one end, between 9 and 10 is only 5% of the scale while the interval between 1 and 2 occupies 30% of the scale (log 2 == 0.30, log 9 == 0.95). If you can estimate measurements to a half millimeter on a precise ruler, on a one foot slide rule that corresponds to 508 divisions. Three significant digits requires 1000. With some careful interpolation while reading a slide rule it is sometimes possible to get 3 significant digits, especially in the range 1 to 2. It’s not possible to get 3 significant digits between 9 and 10. Another limitation of slide rules is that there are no provisions for addition or subtraction. For this there were mechanical adding machines. Notice too that all calculations are done with numbers in scientific notation. The scales start at 1 and end at 10. When calculating something like 447.8 * 1276, the slide rule is only able to calculate 4.48 * 1.28 for the user, and it gives a result like 5.73. The powers of ten have to be handled in one’s head. Furthermore, one has to understand trig well enough that having the sin only from 0 to 90 is good enough. Because slide rules don’t give very precise answers, tables of logarithms were used for calculations requiring 4,5, or 6 digits of significance.