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The National Security Agency assured Americans last week that it only surveils a tiny percentage of the web data it collects. But it turns out the NSA screwed up the math, and that percentage was off by an order of magnitude.

That error is in a document released by the agency on the heels of the president's speech earlier this month announcing measures to review NSA surveillance. We described the math at stake last week, but the pertinent section is this:

Unfortunately, if you do the math in suggested by that paragraph, you don't get that tiny percentage, 0.00004 percent, or 4 parts per 10 million. It's actually 0.0004 percent, with one fewer zero — or 10 times as much as the NSA suggested. It's ten dimes on the basketball court, not one. (See the math at the bottom of this post.)

That's significant largely because of the weight the NSA puts on its percentages. In a New York Times article last Friday, the agency used similar tiny numbers to respond to The Washington Post's blockbuster report indicating that it had repeatedly violated Americans' privacy. (We spotted this via Mother Jones' Kevin Drum.)

The official, John DeLong, the N.S.A. director of compliance, said that the number of mistakes by the agency was extremely low compared with its overall activities. The report showed about 100 errors by analysts in making queries of databases of already-collected communications data; by comparison, he said, the agency performs about 20 million such queries each month.

Twenty million queries, as Drum points out, is a lot of daily queries (or, if you prefer, database searches). It's about 666,000, in fact, in a 31-day month. That's about seven queries every second. (How the NSA defines "query" in this context isn't clear.) In the context of the amount of data the NSA processes, it's also significant. Each day, using the 0.025 percent of 1.6 percent figure above, the government reviews about 7.304 terabytes of data. If you're curious, the ratio of data reviewed to number of queries is about 12.2 megabytes — meaning that the government sets aside 12 megabytes for every query it runs.