Precipitation measured by the National Weather Service is used using a well built and precise gauge. A rain gauge should not be near any obstructions such as trees and buildings. Precipitation is always measured to the nearest 100th of an inch. A tipping bucket range gauge will reset each time a 100th of an inch adds up and the number of tips will equal to entire precipitation event.
To verify how much precipitation a NWS office measures, go to the website below. Click "graphical" next to the state of interest. When the map comes up then click the city of interest. There will be columns for 1 hr, 3 hr and 6 hr precipitation. Each interval will list the amount of precipitation in that time increment. To get storm total precipitation then add all the increments (i.e. each 6 hr precipitation) together.
When the precipitation is snow it is melted down to yield the liquid equivalent. When snow is reported it will be given to the nearest 10th of an inch. Since snows have different densities, equal snow depths can have different liquid equivalents. Thus it is important to look at both the amount of snow and the liquid equivalent to get an idea if it is a dry snow or a wet snow. Snow is measured for an event by taking a ruler and measuring the depth at different spots and then finding the average. This is done since wind will cause the snow depth to vary over a surface. In very strong wind it can be difficult to get a precise snow depth. Often weather watcher networks are used to create and supplement a map or chart of the snow totals for an event across a region. To get these results you can use the NWS website given above. On the page with the map of cities, click link that says "public information" to get the storm reports.