No, a woman continues to have her periods in spite of the use of contraception. However, they can be used to delay your period or choose when you want it to start each month.
To put it simply, birth control pills work by "imitating" the natural menstrual cycle, and this is the reason why women who use them still experience bleeding similar to that of periods, although it is not an actual period.
A pack of birth control pills contains 28 pills, out of which only 21 are active pills (i.e. they contain hormones). Inactive pills are actually a placebo used to maintain the routine of taking one pill each day.
The woman will experience bleeding during the days when she is taking the inactive pills. This bleeding occurs as a response of the body to stopping the reception of the hormones that where present on the active pills.
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