Why does the official unemployment rate understate the real unemployment rate? Provide two reasons.

The survey system used to collect unemployment data relies on a precise definition of unemployment, which may not capture what we are interested in, and a precise wording of the questions asked of the respondent, which may also not lead us to the measure of prime interest.
How is the official definition of unemployment misleading about unemployment?
The unemployment rate is defined as number of people that do not have a job but are actively seeking one, divided by the sum of these people and those who have jobs. Thus, the unemployment rate, by definition, excludes people without jobs but not actively seeking one. This would be fine if it only excluded people who do not want to work. It is misleading because it excludes people who would take a job if one were offered, but are not looking either because the prospects for success have become so slim or they have run out of resources to conduct a search.
How is the method used to collect unemployment data misleading about unemployment?
The precise question asked is whether the respondent worked for at least an hour during the previous week. If the answer is yes, the respondent is counted as employed. If the answer is no, he or she is counted as unemployed. A person who worked 2 hours but was looking for a 40-hours a week job is counted as employed. She is really underemployed, and this fact would be valuable to know.