If I need to mention the year and the century how do I say that in one sentence?
They moved abroad in the 70s in the twentieth century.
They have a collection of paintings painted in the 70s in the twentieth century.
If I need to mention the year and the century how do I say that in one sentence?
They moved abroad in the 70s in the twentieth century.
They have a collection of paintings painted in the 70s in the twentieth century.
The clearest and most concise way would be "in the 1970s" (pronounced "nineteen seventies").
If you want to mention a decade within the last 100 years, such as the 1970s, you merely say the decade.
I moved to Australia in the seventies.
If the decade is from more than 100 years ago, such as 1870, you would include the century.
My grandparents moved to Australia in the eighteen seventies.
Normally, "the seventies" means the 1970s. There are rare occasions where it could mean (for example) the 1870s - this is unusual, but should be obvious from context, e.g.
The British suffragists pushed forward enthusiastically for some twenty years, but the failure to achieve success in 1885, when the third Reform Bill was passed giving the agricultural labourer the vote, seemed to take the heart out of our early suffragists, and the movement died down again. Meanwhile, in the nineties the American women were full of life and enthusiasm, winning victory after victory in State after State. (= eighteen nineties) ( https://spartacus-educational.com/USAWstanton.htm )
If you feel that there is any ambiguity about which century you are discussing, simply use the full form ("1970s"/"nineteen seventies" rather than "seventies"/"'70s"). But in the vast majority of cases it is obvious.
It would be unidiomatic to say "the seventies of the nineteenth century" or the like. Googling finds some such expressions, but many of them seem to be written by non-native speakers or appear in translations from other languages.
When discussing centuries, as in Norwegians came to the New World in the eleventh century, you may have to resort to some old fashioned sounding sentences. I would say Hrvald the Norwegian sailed the ocean in the ninety second year of the eleventh century (1092), or if you want to get really uncommon, ... sailed the ocean in the ninety second year of the second millennium.