Difference between 两 and 二? I know both mean "two," but what differentiates the two?

If there is a difference, when do I use 两 and when do I use 二?
according to 《现代汉语规范词典》：


  现代“二”和“两”的用法区别主要是：1.当作数字读或在数学中，用“二”不用“两”，如“一、二、三、四” “一加一等于二” “一元二次方程”。2.序数、小数、分数中用“二”不用“两”，如“第二” “二嫂” “零点二” “二分之一”。3.在一般量词前，个位数用“两”不用“二”，多位数中的个位数用“二”不用“两”，如“两个人” “两只” “两条” “两次” “一百五十二人” “十二次”。4.在传统的度量衡单位前“二” “两”都可用，只是在质量单位“两”前用“二”不用“两”，属于特例。如“二（两）亩地” “二（两）尺布” “二两酒（不说‘两两酒’）”。在我国法定计量单位和某些非法定计量单位前多用“两”，如“两吨” “两公里” “两（二）米”。5.在多位数中，百位、十位、个位用“二”，千位以上多用“两”，但首位以后的百、千、万前多用“二”，如“二百二十二” “两千元” “两亿人” “三万二千二百人”。㊁见“俩”。


translation:

Major different of "二" and "两" in contemporary Chinese: 1. As a number or in mathematics, uses "二" but not "两". 2. In ordinal, decimal numbers and fractional numbers, uses "二" but not "两". 3. When used with normal counter word, for single digit number, uses "两" but not "二". For multiple digit numbers, uses "二" but not "两" in the digit in units. 4. When used with Chinese traditional units of measurement, both of them can be used. An exception is when "两" is used as a unit, only "二" is used. When used with official and unofficial unit of measurement, "两" is often used. 5. For digits other then the digit of unit in multiple digit numbers, "两" is preferred.