Hello, I saw you question, its interested me also, so i do some quick research (aka. Google it) Most of the people said that the reason that "一" pronounce " Yao" is created for military purposes to avoid misunderstanding, so they created a different one to distinguish it. In my experience, it sure did does that. you can tell that its really easy to make people confused when you try to say" 1EE11E". Back to your question, I'll said you can use "yao " whenever you want to avoid people to misunderstanding by the pronunciation (but only used as number). and... all of this are what I found and comprehended, not sure if its 100% right... I'm willing to learn more as well.

房间号，106房间，yao1/yi1 ling1 liu6 fang2 jian1. 三位的公交车号码 317路 san3 yao1/yi1 qi7 lu4. But most of time if the first number is one, we read it yao1 for telephone or QQ number. 15872152740. yao1 wu5 ba1****** And double one we read yao1 yao1, because yi1 yi1 is not easy to pronounce. 15674201128. ******yao1 yao1 er2 ba1 But when it comes to room number or bus number, it is not that necessary to read yao1, yi1 also can be read.

Dear Alan, Well, you just need to keep in mind that ' 一" can be pronounced "yao", which is casual and informal. A typical case is the police number: 110, we usually pronounce it " yao yao ling", not "yi yi ling". We read " yao" when " 一“ is used in the phone number. But do not worry, in most case, people can understand it in both way. I recommend that you pronounce " yi" if you are not sure. Take it easy. William

关于"幺、两、三、四、五、六、拐、八、勾、洞"的解释 　　第一种：1、2、3、4、5、6、7、8、9、0这十个数字在军事上广泛运用，各军兵种无一例外。特别在炮兵通讯中大量使用，由于军队中人员来自山南海北，口音有所不同，如1和7，6和9等，特别容易听错。作战和训练时大量与数字打交道：方向多少?距离多少?坐标多少?都离不开这十个数字，来不得半点差错，弄不好打到自己人头上。0、1、2、7、9的声母由于发音部位和发音方法不同，在发音上无法发出很大的声音。由于战场环境噪声大，使用电子通信设备时，话筒的频率响应对这几个数字的增益比较低，使发射机功率达不到要求。所以必须对其发音进行改进。于是约定俗成，数字军语使用中改动了1(幺)、2(两)、7(拐)、9(勾)、0(洞),3、4、5、6、8读音未改。十个数字念成：幺、两、叁、肆、伍、六、拐、八、勾、洞。如此这般改动，朗朗上口，不容易出现差错。 　　 　　第二种：词典中对幺、两、洞有解释： 　　幺：数目中的“一”(只能单用,不能组成合成数词,也不能带量词,旧时指色子和骨牌中的一点，现在说数字时也用来代替“一”)。如：幺幺三(113)。另麻将用语，幺万、幺条、幺饼、幺鸡、幺喜、幺牌。 　　两：数目，二。一般用于量词和“个、半、千、万、亿”前：两个黄鹂。两本书。 　　洞：口令中用以代替数目中的“零”。如：洞洞八(008)。 　　至于拐(7)、勾(9)词典中未有解释，《军语》也无从寻觅。现斗胆解释如下，还望高人指点。　 　　拐：军语中代替数目中的“七”、“7”。取“7”字形象拐棍、拐杖。如：拐洞拐(707)。 　　勾：军语中代替数目中的“九”、“9”。源自猜拳划拳。一人伸出几个手指,另一个人同时伸出手指或拳头,按事先约定的规定决定输赢。通常食指作勾状，余指合拢表示“9”，勾代表“9”由此演变尔来。如：勾两勾(929)。 　　第三种：猜拳划拳我国历史悠久。如：《儒林外史》中有“当夜猜三划五,吃了半夜,把二百文都吃完了”的记述。