Left: Huilü 匯率 “exchange rates,” drawn after the real-world application Huilü 匯率 available on Android™ everywhere on Google Play. Right: the list of lü 率 under the heading “Norms for Grain Conversion” 粟米之法 at the opening of The Nine Chapters, chapter 2, as represented in the form the same sort smartphone app. On the left, the quantity entered is 91.150 TWD, and on the right it is 7 dou 8 sheng (= 78 sheng) of unhulled millet, as per The Nine Chapters, problem 2.16. The modern lü—a “rate”—comprises the juxtaposition of two quantities, the one of which is normally pegged at 1, and the other expressed as a decimal fraction (i.e. “1 USD : 30.485 TWD”). To find the equivalent of the starting value of 91.150 TWD in USD, one converts via the rule of three thus: 91.150 TWD × 1 USD ⁄ 30.485 TWD = 2.9900 USD. The pre-modern lü, by contrast is a single integer value assigned to an element in a larger list (i.e. “unhulled millet lü: fifty” 粟率五十). To find the equivalent of the starting value of 78 sheng unhulled millet in fermented soy, one also converts via the rule of three—the “ ‘suppose you have’ procedure” 今有術—but one does so using the simpler integer values of the appropriate lü: 78×63⁄50=98 14/50 sheng fermented soy.