WASHINGTON — Growing numbers of Americans are going cashless, but demands to finally put a woman on paper currency persist. And now the Treasury has announced that a portrait of a woman, to be determined soon, will grace the $10 bill.

The note will continue to have some image, also to be determined, of the current $10 honoree, Alexander Hamilton, a founding father (there were, of course, no mothers) and Treasury secretary to President George Washington (he of the $1 bill). Treasury Secretary Jacob J. Lew, who by law makes the selection of an honoree, will disclose his choice by the end of the year. The new note will appear in 2020 — the 100th anniversary of the 19th Amendment, which gave women the right to vote.

The only criterion under law is that the chosen person must be dead, but the Treasury said Mr. Lew was looking for a woman “who was a champion for our inclusive democracy.” That would include the abolitionist Harriet Tubman, who was the top choice on social media of a campaign to put a woman on the $20 bill.

Image Ten-dollar bills at the National Archives in Washington in 2006. The note in 2020 will feature a yet-to-be-named woman alongside Alexander Hamilton. Credit... Alex Wong/Getty Images

Putting a woman on paper notes is certain to be an honor more long-lived than that accorded two history-making women whose images were put on coins. Susan B. Anthony, the social reformer, appeared on silver dollars minted from 1979 to 1981, and again in 1999, and Sacagawea, the Shoshone guide to the Lewis and Clark expedition, was featured on gold-colored dollar coins from 2000. Both coins, which were often confused with quarters, proved unpopular, and production of them was stopped.