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Yes, the best method is to count the actual days. However, you may first wish to estimate the number of days using a typical week or month. If you find the total is close to half the year (183 days for 2016), then you may want to go back and count the actual days for each month. Otherwise, you can use your estimate.

Note that the question "How many days with you?" is answered in number of months. To qualify for the dependent exemption, you need half the year (ie: six months or more).