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WASHINGTON — Many states that posted big population gains in the 2010 census are seeing their decade-long growth fizzle, hurt by a prolonged economic slump that is stretching into larger portions of the South and West.

New 2011 estimates released Wednesday by the Census Bureau are the first state numbers since the 2010 count, which found the nation’s population growth shifting to the Sun Belt.

As a whole, the U.S. population grew by 2.8 million, reaching 311.6 million people.

That growth of 0.92 percent was the lowest since the mid- 1940s, hurt by fewer births and less immigration following the recent recession. The government previously reported that from 2000 to 2010, the nation grew 9.7 percent, the lowest since the Great Depression.

“The nation’s overall growth rate is now at its lowest point since before the baby boom,” said Census Bureau director Robert Groves.

Washington, D.C., grew faster than any state, climbing by 2.7 percent from April 2010 to July of this year. It was the first time the District led states in growth since the early 1940s. Texas saw the next-fastest growth, followed by Utah, Alaska, Colorado and North Dakota.

States that prospered during the real-estate boom, such as Arizona, Nevada and Florida, were already beginning to show a drop in growth when their populations were officially counted a year ago. Since then, the slowdown has spread to other burgeoning areas whose populations had previously withstood much of the dampening effects of the sluggish economy.

They include Georgia, South Carolina, Utah and Idaho, whose annual growth over the past two years is now the weakest of any time in the past decade.

Texas, the big 2010 winner owing to a diversified economy that attracted new residents during the recession, is seeing its growth slow as fewer people move there.

In contrast, Democratic-leaning states such as California and New York are losing fewer residents to other states than before.

In all, 38 states showed lower growth in 2010 and 2011 than in either of the previous two years during the recession.

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