There appears to be an astonishing lack of references as to which period the 1900s refer to.
Wikipedia claims that the term 1900s can either refer to the period between 01/01/1900 and 12/31/1909 or for the years 1900-1999.
While the Mnemonic Dictionary defines 1900s as belonging to the first decade of the 20th century
The 20th century
is also referred to as the 1900s by Wikipedia
Although this expression is commonly used to cover the first decade, I could find no authoritative source that actually defined the precise length of time or precluded the years 1910 to 1918.
Below is an Ngram chart plotting the frequency of usage of the following terms: “1900s”, “early 1900s” and “early 20th century”. The term 1900s dominates its two rivals from the start. Interestingly, it appears to have enjoyed a sharp rise around 1978 while reaching a peak in 1984. This might have been influenced by George Orwell's dystopian novel Nineteen Eighty-Four, or be just coincidence. Despite its sudden drop, the term 1900s picked up and enjoyed a continuous surge until the year 2000.