Originally, October WAS the 8th month of the year and september was the 7th (as sept~ is 7). As you may know, the two main calendars are the Julian Calendar (considered outdated) and the Gregorian Calendar (used in daily life; same as Julian Calendar, except that all centuries are not leap years - only those divisible by 400, this is more scientifically accurate). As the name suggests, the Julian Calendar was devised by Julius Caeser. He corrected the number of days in each month, renamed the months Iunius to June (after Roman Goddess Juno) and Quintilius (Quint~ is five in Latin) to July (after himself, such was his pride) Sextilis to August (after Augustus Caeser, his nephew and general) and shifted the months January and February (which were at the last after December) to the top. This shifting of the two months pushed the months September and October two steps down the calendar.

->According to the calendar we use in daily life, the Gregorian Calendar (devised by Pope
   Gregory), the leap year rule does not apply to centuries. Instead of being divisible by 4,
   centuries have to be divisible by 400 to be counted as leap centuries, with an extra day in    February, i.e. the yea 2000 was a leap year, but 1900 and 1800 and 1700 were not.
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people usually believe that july and august were added to the roman calendar in honor of julius and augusta. the name of the fifth month quintilius and the sixth as sextilius were changed to julius and augusta to honor the caesar.

the original  roman calendar had just 10 months,march-martius and then december for the next 61 days of winter but later arrangements were made in such a way...
martius,aprilis,maius,lunius ,quintilius,sextilius,september ,october, november december as 10 monts later lanuarius(jan) and februarius(feb) were added later january was called as "the first month" and "the renewal of the sun"later making september 9th ,october the 10th, november the 11th and december the 12
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january and february were not added they were present after december
oh srry abt the mistake...
a long time ago the Roman Calendar had 10 months, but that was centuries before july and august were added
and January became the first month which was named after Janus, the two faced goddess.