XKCD 2585: Rounding

	A	B	C	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T
1
2
3
4	starting:		end:		numbers used to derive ratios		45	20.1168	39.10393	11	6	72.42048	360	22
5	16		0
6	total increase:		0.00%
7	no. of steps:		2
8					step:	1	mph	m/s	knots	fathoms/sec	furlongs/min	km/h	furlongs/hour	yards/sec
9	percentage increases:
10	1		N/A		ratios to mph:		1	0.44704	0.8689762222	0.2444444444	0.1333333333	1.609344	8	0.4888888889
11	2	T17	0.00%
12	3	T22	0.00%		starting values:		16	7.15264	13.90361956	3.911111111	2.133333333	25.749504	128	7.822222222	error checking:		total steps	end value	valid % increases
13	4	T27	0.00%	copy start	step:	2	16	7	14	4	2	26	128	8
14	5	T32	0.00%	\|			1	0.9786596278	1.00693204	1.022727273	0.9375	1.009728187	1	1.022727273	no increase:	0
15	6	T37	0.00%	\|	max:	1.022727273	0	0	0	1	0	0	0	1	error, step no.:	1	2
16	7	T42	0.00%	\|	new val mph:	32.72727273	0	0	0	16.36363636	0	0	0	16.36363636	end value:
17	8	T47	0.00%	copy end	new values:		32.72727273	14.6304	28.43922182	8	4.363636364	52.66944	261.8181818	16	gain:	2.27%			0.00%
18	9	T52	0.00%	copy start	step:	3	33	15	28	8	4	53	262	16
19	10	T57	0.00%	\|			1.008333333	1.025262467	0.9845557723	1	0.9166666667	1.006276125	1.000694444	1	no increase:	0
20	11	T62	0.00%	\|	max:	1.025262467	0	1	0	0	0	0	0	0	error, step no.:	2	0
21	12	T67	0.00%	\|	new val mph:	33.55404438	0	33.55404438	0	0	0	0	0	0	end value:			0
22	13	T72	0.00%	copy end	new values:		33.55404438	15	29.15766673	8.202099738	4.473872584	54	268.432355	16.40419948	gain:	2.53%			0.00%
23	14	T77	0.00%	copy start	step:	4	34	15	29	8	4	54	268	16
24	15	T82	0.00%	\|			1.013290667	1	0.9945926151	0.97536	0.89408	1	0.9983893333	0.97536	no increase:	0
25	16	T87	0.00%	\|	max:	1.013290667	1	0	0	0	0	0	0	0	error, step no.:	4	0
26	17	T92	0.00%	\|	new val mph:	34	34	0	0	0	0	0	0	0	end value:			0
27	18	T97	0.00%	copy end	new values:		34	15.19936	29.54519156	8.311111111	4.533333333	54.717696	272	16.62222222	gain:	1.33%			0.00%
28	19	T102	0.00%	copy start	step:	5	34	15	30	8	5	55	272	17
29	20	T107	0.00%	\|			1	0.9868836583	1.015393654	0.9625668449	1.102941176	1.005159282	1	1.022727273	no increase:	0
30	21	T112	0.00%	\|	max:	1.102941176	0	0	0	0	1	0	0	0	error, step no.:	8	0
31	22	T117	0.00%	\|	new val mph:	37.5	0	0	0	0	37.5	0	0	0	end value:			0
32	23	T122	0.00%	copy end	new values:		37.5	16.764	32.58660833	9.166666667	5	60.3504	300	18.33333333	gain:	10.29%			0.00%
33	24	T127	0.00%	copy start	step:	6	38	17	33	9	5	60	300	18
34	25	T132	0.00%	\|			1.013333333	1.014077786	1.012685937	0.9818181818	1	0.9941939076	1	0.9818181818	no increase:	0
35	26	T137	0.00%	\|	max:	1.014077786	0	1	0	0	0	0	0	0	error, step no.:	16	0
36	27	T142	0.00%	\|	new val mph:	38.02791696	0	38.02791696	0	0	0	0	0	0	end value:			0
37	28	T147		copy end	new values:		38.02791696	17	33.04535562	9.295713036	5.070388929	61.2	304.2233357	18.59142607	gain:	1.41%			0.00%
38	29	T152		copy start	step:	7	38	17	33	9	5	61	304	19
39	30	T157		\|			0.9992658824	1	0.9986274736	0.9681882353	0.9861176471	0.9967320261	0.9992658824	1.021976471	no increase:	0
40	31	T162		\|	max:	1.021976471	0	0	0	0	0	0	0	1	error, step no.:	32	0
41	32	T167		\|	new val mph:	38.86363636	0	0	0	0	0	0	0	38.86363636	end value:			0
42	33	T172		copy end	new values:		38.86363636	17.3736	33.77157591	9.5	5.181818182	62.54496	310.9090909	19	gain:	2.20%			0.00%
43				copy start	step:	8	39	17	34	10	5	63	311	19
44				\|			1.003508772	0.978496109	1.006763797	1.052631579	0.9649122807	1.007275406	1.000292398	1	no increase:	0
45				\|	max:	1.052631579	0	0	0	1	0	0	0	0	error, step no.:	64	0
46				\|	new val mph:	40.90909091	0	0	0	40.90909091	0	0	0	0	end value:			0
47				copy end	new values:		40.90909091	18.288	35.54902727	10	5.454545455	65.8368	327.2727273	20	gain:	5.26%			0.00%
48				copy start	step:	9	41	18	36	10	5	66	327	20
49				\|			1.002222222	0.9842519685	1.012685937	1	0.9166666667	1.002478857	0.9991666667	1	no increase:	0
50				\|	max:	1.012685937	0	0	1	0	0	0	0	0	error, step no.:	128	0
51				\|	new val mph:	41.42806107	0	0	41.42806107	0	0	0	0	0	end value:			0
52				copy end	new values:		41.42806107	18.52000042	36	10.12685937	5.523741476	66.67200151	331.4244885	20.25371874	gain:	1.27%			0.00%
53				copy start	step:	10	41	19	36	10	6	67	331	20
54				\|			0.9896673642	1.025917903	1	0.9874729798	1.086220278	1.004919584	0.9987191998	0.9874729798	no increase:	0
55				\|	max:	1.086220278	0	0	0	0	1	0	0	0	error, step no.:	256	0
56				\|	new val mph:	45	0	0	0	0	45	0	0	0	end value:			0
57				copy end	new values:		45	20.1168	39.10393	11	6	72.42048	360	22	gain:	8.62%			0.00%
58				copy start	step:	11	45	20	39	11	6	72	360	22
59				\|			1	0.9941939076	0.9973422109	1	1	0.9941939076	1	1	no increase:	0
60				\|	max:	1	1	0	0	1	1	0	1	1	error, step no.:	257	0
61				\|	new val mph:	225	45	0	0	45	45	0	45	45	end value:			0
62				copy end	new values:		225	100.584	195.51965	55	30	362.1024	1800	110	gain:	0.00%			0.00%
63				copy start	step:	12	225	101	196	55	30	362	1800	110
64				\|			1	1.004135847	1.002456786	1	1	0.9997172071	1	1	no increase:	0
65				\|	max:	1.004135847	0	1	0	0	0	0	0	0	error, step no.:	514	0
66				\|	new val mph:	225.9305655	0	225.9305655	0	0	0	0	0	0	end value:			0
67				copy end	new values:		225.9305655	101	196.3282893	55.22747157	30.1240754	363.6	1807.444524	110.4549431	gain:	0.41%			0.00%
68				copy start	step:	13	226	101	196	55	30	364	1807	110
69				\|			1.000307327	1	0.9983278554	0.9958811881	0.9958811881	1.00110011	0.9997540594	0.9958811881	no increase:	0
70				\|	max:	1.00110011	0	0	0	0	0	1	0	0	error, step no.:	1028	0
71				\|	new val mph:	226.179114	0	0	0	0	0	226.179114	0	0	end value:			0
72				copy end	new values:		226.179114	101.1111111	196.544272	55.28822786	30.1572152	364	1809.432912	110.5764557	gain:	0.11%			0.00%
73				copy start	step:	14	226	101	197	55	30	364	1809	111
74				\|			0.9992080879	0.9989010989	1.002318704	0.9947868132	0.9947868132	1	0.9997607473	1.00383033	no increase:	0
75				\|	max:	1.00383033	0	0	0	0	0	0	0	1	error, step no.:	2056	0
76				\|	new val mph:	227.0454545	0	0	0	0	0	0	0	227.0454545	end value:			0
77				copy end	new values:		227.0454545	101.4984	197.2971014	55.5	30.27272727	365.39424	1816.363636	111	gain:	0.38%			0.00%
78				copy start	step:	15	227	101	197	56	30	365	1816	111
79				\|			0.9997997998	0.9950895778	0.9984941423	1.009009009	0.990990991	0.9989210558	0.9997997998	1	no increase:	0
80				\|	max:	1.009009009	0	0	0	1	0	0	0	0	error, step no.:	4112	0
81				\|	new val mph:	229.0909091	0	0	0	229.0909091	0	0	0	0	end value:			0
82				copy end	new values:		229.0909091	102.4128	199.0745527	56	30.54545455	368.68608	1832.727273	112	gain:	0.90%			0.00%
83				copy start	step:	16	229	102	199	56	31	369	1833	112
84				\|			0.9996031746	0.9959692538	0.9996255035	1	1.014880952	1.000851456	1.00014881	1	no increase:	0
85				\|	max:	1.014880952	0	0	0	0	1	0	0	0	error, step no.:	8224	0
86				\|	new val mph:	232.5	0	0	0	0	232.5	0	0	0	end value:			0
87				copy end	new values:		232.5	103.9368	202.0369717	56.83333333	31	374.17248	1860	113.6666667	gain:	1.49%			0.00%
88				copy start	step:	17	233	104	202	57	31	374	1860	114
89				\|			1.002150538	1.000608062	0.9998170054	1.002932551	1	0.9995390361	1	1.002932551	no increase:	0
90				\|	max:	1.002932551	0	0	0	1	0	0	0	1	error, step no.:	8225	0
91				\|	new val mph:	466.3636364	0	0	0	233.1818182	0	0	0	233.1818182	end value:			0
92				copy end	new values:		466.3636364	208.4832	405.2589109	114	62.18181818	750.53952	3730.909091	228	gain:	0.29%			0.00%
93				copy start	step:	18	466	208	405	114	62	751	3731	228
94				\|			0.9992202729	0.9976823073	0.9993611222	1	0.9970760234	1.000613532	1.000024366	1	no increase:	0
95				\|	max:	1.000613532	0	0	0	0	0	1	0	0	error, step no.:	16450	0
96				\|	new val mph:	466.6497654	0	0	0	0	0	466.6497654	0	0	end value:			0
97				copy end	new values:		466.6497654	208.6111111	405.5075502	114.0699426	62.21996872	751	3733.198123	228.1398853	gain:	0.06%			0.00%
98				copy start	step:	19	467	209	406	114	62	751	3733	228
99				\|			1.00075053	1.001864181	1.001214403	0.9993868442	0.9964646605	1	0.9999469294	0.9993868442	no increase:	0
100				\|	max:	1.001864181	0	1	0	0	0	0	0	0	error, step no.:	32900	0