Counting a single day as part of two consecutive, mutually exclusive periods of time: Rosh HaShanah 10b
Considering the first/last day of the year to be the entire year, in calculating a king's reign: Rosh HaShanah 2b, 7b
Considering 1 day of a month, to be equivalent to passage of the entire month: Rosh HaShanah 10b
Considering 1 day of the year to be equivalent to passage of the entire year: Rosh HaShanah 10b, 12b
Considering 30 days of the year to be equivalent to passage of the entire year: Rosh HaShanah 10b, 12b
Specific Cases
Considering one day of the year to be the entire year, in calculating the age of an animal to be fit for a specific offering: Rosh HaShanah 10a-b
Considering one day of the year to be the entire year, in calculating the growth of a plant for its status vis-a-vis prohibitions on using produce of a tree's first 3 years: Rosh HaShanah 10a-b
Counting the remainder of the 1st day when a menstruating woman sees blood, as the 1st day of her 7-day period of waiting: Rosh HaShanah 10a
Counting part of the 7th day after a menstruating woman sees blood, as the entire 7th day to complete the period of waiting: Rosh HaShanah 10a