The Gold Dollars produced for the 1903-04 Louisiana Purchase Exposition come in two types: Thomas Jefferson portrait (obverse) and William McKinley portrait (obverse); the two types share a common reverse.
The dual dates of "1803-1903" on the common reverse can lead to at least two false conclusions:
1) The LPE was held in 1903.
Incorrect.
The Exposition's opening was initially planned for April 1903 - in August 1901 US President William McKinley issued Proclamation 464 which announced the Exposition's opening in 1903 and extended an invitation to "all nations of the earth" to participate and exhibit at the Exposition - but it was pushed back to April 1904 to enable greater participation by exhibitors and to ensure the Exposition's grounds were completed. The Louisiana Purchase Centennial was marked by the Exposition Company on April 30, 1903 - it also dedicated the Exposition - but the LPE did not truly open until April 1904.
2) The coins were struck in 1903.
Some were, but not all.
The US Mint at Philadelphia struck 75,080 of the LPE coins in 1902 and 175,178 in 1903 - a total of 250,258 (250,000 were authorized, the overage was used for assay purposes). Mint records listing the exact split between the two types do not exist today, but most dealers/collectors operate under the assumption of a 50/50 split for the types in each year.
1903 Louisiana Purchase Exposition Gold Dollar - Jefferson Type
1903 Louisiana Purchase Exposition Gold Dollar - McKinley Type

For other of my posts about commemorative coins and medals, including more on the LPE Gold Dollars discussed here, see:
Commems Collection.