Meredith Angwin blogs that a pico is the metric term for one-trillionth, i.e., ten-to-the- minus twelve, or one-thousandth of a billionth. In other words, it takes one thousand pico-meters to equal one billionth of a meter. But of course he is not talking about meters. He is talking about radiation here. There is almost nothing else that you can measure in picos. One gram of radium releases one curie of radiation. Radiation limits of various sorts, e.g., tritium or strontium 90 in water, are generally expressed as pico-curies. Trillionths of a curie. Why do we measure them as trillionths of a curie. We do not just measure them as parts-per-trillion of water, or as grams of material. Basically, such measurements are just not practical. We cannot measure grams-per-liter effectively at the trillionth level. A pico is just too small.
When you are trying to measure something at low parts per billion levels, everything gets in the way of getting a decent measurement. For example, ions will cling to the side of the flask, and the flask may be shedding parts per million of other ions. In short, measuring the ion content of ultra-pure water, measuring individual ions at the parts per billion level is a field of highly specialized expertise.
Below the parts per billion level, it is even harder to measure the presence of most ions. Measuring parts per trillion is close to impossible, though not impossible. However, if the ion is radioactive, it is relatively easy to measure very low levels of the material. You can measure parts per billion and smaller. There is that pico term again. You can measure pico curie levels. The ease of measuring radiation makes it easy to scare people with the so-called fact that radioactive ions are present. If a radioactive ion is present, you can find it easily...but at very low levels.
A few anti-nuclear organizations have produced some scare-story videos about nuclear energy. David Ropeik has written an article about these videos.
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