top scale is moved to the 2 on the bottom scale. The answer, 14, is read off the bottom scale where 7 is on the top scale. Since the 7 is above the second set of numbers the result must be multiplied by 10. Thus, even though the answer directly reads 1.4, the correct answer is 1.4 x 10 = 14. To multiply 88x20, the 1 on the top scale is moved to the 2 on the bottom scale. Since 2 represents 20 all numbers in that scale are multiplied by 10, thus any answer in the second set of numbers is multiplied by 100. Since 8.8 in the top scale represents 88, the answer must additionally be multiplied by 10. The answer answer directly reads 1.76. Multiply by 100 and then by 10 to get the actual answer: 1,760. In general, the 1 on the top is moved to a factor on the bottom, and the answer is read off the bottom where the other factor is on the top. This works because the distances from the "1" are proportional to the logarithms of the marked values. Division The illustration below demonstrates the computation of 5.5/2. The 2 on the top scale is placed over the 5.5 on the bottom scale. The 1 on the top scale lies above the quotient, 2.75. There is more than one method for doing division, and the method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the 1 at either end. With more complex calculations involving multiple factors in the numerator and denominator of an expression, movement of the scales can be minimized by alternating divisions and multiplications. Thus (5.5×3)/2 would be computed as (5.5/2)×3 and the result, 8.25, can be read beneath the 3 in the top scale in the figure above, without the need to register the intermediate result for 5.5/2. Other operations In addition to the logarithmic scales, some slide rules have other mathematical functions encoded on other auxiliary scales. The most popular are trigonometric, usually sine and tangent, common logarithm (log) (for taking the log of a value on a multiplier scale), natural logarithm (ln) and exponential (ex) scales. Some rules include a Pythagorean ("P") scale to solve triangles. Others feature scales for calculating hyperbolic functions. On linear rules, the scales and their labeling are highly standardized, with