to write something on a piece of paper so that you do not forget it

Did you write down Jo's phone number? 你把乔的电话号码记下来了吗？

to show in a company's accounts (= financial records) that something is worth less than it was before

The building cost £700,000 to build, but it was written down to £300,000. 修建这栋楼花费了70万英镑，现在其账面价值只有30万镑了。