WASHINGTON — Let the count begin.

More than 120 million U.S. census forms begin arriving Monday in mailboxes around the country, in the government’s once-a-decade population count that will be used to divvy up congressional seats and more than $400 billion in federal aid. Fast-growing states in the South and the West could stand to lose the most because of lower-than-average mail participation rates in 2000 and higher shares of Hispanics and young adults, who are among the least likely to mail in their forms.

Did those $2.5 million Super Bowl ads work? Stay tuned.

“When you receive your 2010 census, please fill it out and mail it back,” said Census Bureau director Robert Groves, who was set to kick off the national mail-in campaign Monday in Phoenix, Ariz., a state which could gain up to two U.S. House seats because of rapid immigrant growth in the last decade.

Groves is urging cities and states to promote the census and improve upon rates in 2000, when about 72 percent of U.S. households returned their forms. If everyone who receives a census form mails it back, the government would save an estimated $1.5 billion in follow-up visits.

Speaking in an interview, Groves said real-time census data showed public awareness of the 2010 count had improved since January to levels similar to 2000 at this point, which he called “good news.” Still, he remained particularly concerned about motivating young adults, who were lagging other groups. Many twenty-somethings now on their own were living with their parents in 2000, so they haven’t had the experience of filling out census forms.

“If the American public comes through in the way everyone is capable of, we’ll have a great census,” Groves said.

The next few weeks will be critical. Even as it aims high, the Census Bureau predicts that maybe two-thirds of U.S. households will mail in the form. That’s because it faces special challenges of growing U.S. apathy toward surveys, residents displaced by a high number of foreclosures, as well as immigrants who have become more distrustful of government workers amid a crackdown on illegal immigration.

From May until July, it will send census-takers to each home that doesn’t reply by mail, which sometimes leads to more inaccurate responses.

In 2000, Florida, Georgia, Nevada, Arizona, Texas and North Carolina each had below-average mail participation rates of less than 70 percent, according to newly released census data. Since then, many of these states have seen higher rates of foreclosures and rapid growth of Hispanics or blacks, who are often more reluctant to turn in their forms. Each of these states stand to gain at least one U.S. House seat, with Texas picking up as many as four.

On the other end of the scale, Midwest states such as Wisconsin, Iowa and Nebraska ranked at the top in mail participation, at roughly 80 percent. These states had higher shares of older white residents, who are more likely to view census participation as a civic duty. Iowa could lose one seat based on slowing population growth, while seats for Wisconsin and Nebraska are likely to remain unchanged.

In 2000, the Census Bureau for the first time had a nationwide overcount of 1.3 million people, mostly from duplicate counts of more affluent whites with multiple homes. Still, 4.5 million people were ultimately missed, mostly lower-income blacks and Hispanics.

“The Census Bureau has its work cut out for it,” said William H. Frey, a demographer at the Brookings Institution who analyzed the participation numbers. He noted an irony in which states and counties with high mail-participation rates in 2000 were the ones least likely to see large population gains in recent years.

“This makes it even more incumbent on the dynamic fast-growing parts of the country to improve upon their subpar census participation in 2000, if they are going to receive their just rewards,” Frey said.

As part of its outreach, the Census Bureau for the first time is mailing out bilingual English-Spanish census forms to 13 million households. Census forms are also available upon request in Chinese, Korean, Vietnamese and Russian, and assistance guides are available in 59 languages at www.2010census.gov.

It also is hoping to motivate cities, counties and local communities to get involved. In 2000, both dense urban cities and sprawling rural areas — from Alabama and California to Michigan and New York — faced problems with an undercount, particularly in areas with larger shares of lower-income residents.

Beginning next week, the Census Bureau will publish daily real-time data on 2010 mail-back participation rates for the U.S. broken down by state, county, city and zip code. Ron Loveridge, president of the National League of Cities and the mayor of Riverside, Calif., is challenging mayors to see who can get the highest participation rate.

The 10-question form is one of the shortest in the history of the census. It asks a person’s name, address, phone number, age, race and ethnicity, gender, living arrangements and home ownership. The information is kept strictly confidential under federal law, and the Census Bureau does not share data with other agencies, including law enforcement.

Failure to respond to the census carries a fine of up to $5,000, although that law is rarely enforced.

The mail-back campaign comes after the Commerce Department inspector general, Todd Zinser, last month found the Census Bureau wasted millions of dollars in paying temporary employees who didn’t do the work and overbilled for travel. Zinser urged the bureau to tighten spending controls before it dispatched 650,000 additional temporary employees to visit homes in May.

Groves, who was sworn in as director in July, has said he would keep closer watch over agency spending.

The Super Bowl advertising, part of the bureau’s $133 million media campaign to increase public awareness, was panned as ineffective by media critics and wasteful by Republicans including Sen. John McCain of Arizona. The IG report, however, said the advertising was consistent with government goals of boosting participation in the count.