速算技巧

n	倒数 %	对数	根号	平方	立方	2 的幂	Sn	阶乘
1	100.0%	0.00	1.00	1	1	2	1	1
2	50.0%	0.30	1.41	4	8	4	3	2
3	33.3%	0.48	1.73	9	27	8	6	6
4	25.0%	0.60	2.00	16	64	16	10	24
5	20.0%	0.70	2.24	25	125	32	15	120
6	16.7%	0.78	2.45	36	216	64	21	720
7	14.3%	0.85	2.65	49	343	128	28	5040
8	12.5%	0.90	2.83	64	512	256	36	40320
9	11.1%	0.95	3.00	81	729	512	45	362880
10	10.0%	1.00	3.16	100	1000	1024	55	3628800
11	9.1%	1.04	3.32	121	1331	2048	66	39916800
12	8.3%	1.08	3.46	144	1728	4096	78	479001600
13	7.7%	1.11	3.61	169	2197	8192	91	6227020800
14	7.1%	1.15	3.74	196	2744	16384	105	87178291200
15	6.7%	1.18	3.87	225	3375	32768	120	1307674368000
16	6.25%	1.20	4.00	256	4096	65536	136	20922789888000
17	5.9%	1.23	4.12	289	4913	131072	153	355687428096000
18	5.6%	1.26	4.24	324	5832	262144	171	6402373705728000
19	5.3%	1.28	4.36	361	6859	524288	190	121645100408832000
20	5.0%	1.30	4.47	400	8000	1048576	210	2432902008176640000

特殊分数

1/20~1/10	%% 1/20 = 5.0% %%	1/19 ≈ 5.3%	1/18 ≈ 5.6%	1/17 ≈ 5.9%	1/16 ≈ 6.3%	1/15 ≈ 6.7%	1/14 ≈ 7.1%	1/13 ≈ 7.7%	1/12 ≈ 8.3%	1/11 ≈ 9.1%
1/10~1/4	%% 1/10 = 10.0% %%	1/9 ≈ 11.1%	1/8 = 12.5%	1/7 ≈ 14.3%	1/6 ≈ 16.7%	%% 1/5 = 20.0% %%	2/9 ≈ 22.2%
1/4~1/2	%% 1/4 = 25.0% %%	2/7 ≈ 28.6%	%% 3/10 = 30.0% %%	%% 1/3 ≈ 33.3% %%	3/8 = 37.5%	%% 2/5 = 40.0% %%	3/7 ≈ 42.9%	4/9 ≈ 44.4%
1/2~3/4	%% 1/2 = 50.0% %%	5/9 ≈ 55.6%	4/7 ≈ 57.1%	%% 3/5 = 60.0% %%	5/8 = 62.5%	%% 2/3 ≈ 66.7% %%	%% 7/10 = 70.0% %%	5/7 ≈ 71.4%
3/4~1	%% 3/4 = 75.0% %%	7/9 ≈ 77.8%	%% 4/5 = 80.0% %%	5/6 ≈ 83.3%	6/7 ≈ 85.7%	7/8 = 87.5%	8/9 ≈ 88.9%	%% 9/10 = 90.0% %%

title: 合比分比定理
a/b=c/d=(a+c)/(b+d)=(a-c)/(b-d)