How many immigrants came to the U.S. in 1880? How many in 1890? What
percentage of the population was foreign born in those years?

How many immigrants came to the U.S. in 1880? 

1880 ........................457,257


How many in 1890?

1890 ........................455,302

Source: U.S. Citizenship and Immigration Services
TABLE 1. IMMIGRATION TO THE UNITED STATES: FISCAL YEARS 1820 ? 1999

1880 ........................457,257
1881 ........................669,431
1882 ........................788,992
1883 ........................603,322
1884 ........................518,592
1885 ........................395,346
1886 ........................334,203
1887 ........................490,109
1888 ........................546,889
1889 ........................444,427
1890 ........................455,302

U.S. Citizenship and Immigration Services
http://uscis.gov/graphics/shared/aboutus/statistics/IMM99tables.pdf


DECENNIAL IMMIGRATION TO THE UNITED STATES, 1880-1919
(source: U.S. Bureau of the Census Monograph, no. 7, 1927, pp. 324-25). 
1880-1889   5,248,568
1890-1899   3,694,295
1900-1909   8,202-388
http://web.uccs.edu/~history/fall2000websites/hist153/imgrstats.htm


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What percentage of the population was foreign born in those years?


1880 -  Foreign born population 13.3% of total population.

Source: U.S. Bureau of the Census
http://www.census.gov/population/www/documentation/twps0029/tab01.html



1890 - Foreign- born population 14.8% of total population.
                     
Source: U.S. Bureau of the Census
http://www.census.gov/Press-Release/www/releases/archives/foreignborn_population/000469.html



------------------------------------------------

 
?The 1850 decennial census was the first census in which data were
collected on the nativity of the population. From 1850 to 1930, the
foreign-born population of the United States increased from 2.2
million to 14.2 million, reflecting large-scale immigration from
Europe during most of this period.1 As a percentage of total
population, the foreign-born population rose from 9.7 percent in 1850
and fluctuated in the 13 percent to 15 percent range from 1860 to 1920
before dropping to 11.6 percent in 1930. The highest percentages
foreign born were 14.4 percent in 1870, 14.8 percent in 1890 and 14.7
percent in 1910.?
U.S. Bureau of the Census:Population Division
http://www.census.gov/population/www/documentation/twps0029/twps0029.html

Search criteria:
U.S. Census Bureau
U.S. Citizenship and Immigration Services


I hope you find this helpful!  If anything is unclear with my answer,
please ask for clarification.

Best Regards,
Bobbie7

Thanks so much!