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A decade is a period of ten years; all the decades:

1904-1913, 1915-1924, 1926-1935, 1937-1946, 1948-1957, 1959-1968, 1970-1979, 1981-1990

in the 20th century are decades with no year divisible by 11.

If you want a decade based on a period of 10 years starting with the first ten years of the 20th century (1901-1910), the second ten years and so on, then it is the 9th decade from 1981 to 1990 that has no year divisible by 11.

Alternatively, based on popular culture, it can also be what is known as the 70s, the decade 1970-1979. (Though with this nomenclature the 1st decade of the 20th century, the "noughties", only has the 9 years (1901-1909) unless the last year of the 19th century (namely 1900) is also included.)

If you (or your teacher who set the question) is of the opinion that the 20th century [CE] runs from 1900 to 1999 [CE] (based on the big celebration held in rather a lot of countries for the start of the 21st century CE at midnight between 31/12/1999 CE and 01/01/2000 CE), then the 8th decade of ten years from 1970 to 1979, popularly known as the 70s, has no year divisible by 11.

This opinion is based on a likeness of round numbers and ignores two major facts:

1) when the current year dates were set up by Dennis the little (Dionysius Exiguus) in the year he called 525 AD, zero had not really been invented, and certainly didn't come to Europe until 400-600 years later; he made his first year 1 AD and so his (and our) first century ran from 1 AD to 100 AD, the 2nd from 101 AD to 200 AD and so on with the 20th running from 1901 AD to 2000 AD, the 21st century, and the 3rd millennium, starting at the beginning of the year 2001 AD, after the end of the year 2000 AD. His first century before 1 AD ran from 100 BC to 1 BC - the end of 1 BC being following immediately by the start of 1 AD.

2) To stay with 2000 CE being the first year of the 3rd millennia CE, the 1st millennium must have started in the year 0 CE, or if there is agreement that year 0 doesn't exist, it must have run from the start of 1 BCE, with the 1st millennia BCE running from 1001 BCE to 2 BCE. But if 0 CE exists, then what about the 1st millennium BCE: does it run from 1000 BCE to 1 BCE, or to keep in with the year with all zeros being at the end of the millennium 999 BCE to 0 BCE - ie there are now 2 year zero (0 BCE and 0 CE)?

It also means that ancient historic dates are now wrong - it has only been in the last 40 years (or so - since I was taught at school) that the last year of the 20th century seems to have been changed from 2001 AD to 2000 CE (along with the change in the size of a billion being made a thousand times smaller from a million million to only a thousand million [in the UK]) as 45 BC (etc) when I was taught it must now be 44 BCE or 43 BCE depending upon whether there is only 0 CE or also 0 BCE.

Unless, of course, the first millennium CE only had 999 years (1 CE to 999 CE) instead of 1 thousand along with the first millennium BCE (999 BCE to 1 BCE), which leaves 45 BC = 45 BCE.

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Q: Which decade of the 20th century had no years that were divisible by 11?
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