How much bigger are eukaryotic cells than prokaryotic cells?
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A lot bigger. http://www.life.umd.edu/classroom/bsci424/BSCI223WebSiteFiles/ProkaryoticvsEukaryotic.htm
In general, Eukaryotic cells are a fair bit larger than Prokaryotic cells (if you look at them under the microscope, you can generally see details inside Eukaryotic cells, whereas Prokaryotes are just tiny dots) but... HOW much bigger varies a lot, and, since this is biology we're talking about, there are exceptions:
The largest bacteria (Thiomargarita namibiensis: http://en.wikipedia.org/wiki/Thiomargarita_namibiensis) range in size from 100-200µm, with some specimens reaching 750µm. Flagellates (Eukaryotic single-celled organisms characterised by one or more flagella) are typically only 5-20 µm, and Microsporidia (parasitic single-celled Eukaryotes) are often only 1-4µm.
Most bacteria, however, are only 0.5-5µm in length, which makes them smaller than almost all Eukaryotic cells. Wikipedia claims that they're "about one tenth the size of eukaryotic cells", but I would dispute that. Some Eukaryotic cells can be huge! There are whole organisms visible to the naked eye that are actually one multi-nucleated Eukaryotic cell. Look at this one: http://farm4.staticflickr.com/3093/2529754883_2cfdb9fed8.jpg (each little green umbrella-shaped thing is a single Eukaryotic cell)
Plasmodial slime molds can also reach enormous sizes. I've seen a photo of people measuring one that had been grown so it was several meters long.
Eukaryotic cells are ten times bigger then prokaryotic cells
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... except for the ones that are millions of times bigger, @blacklotus, and the ones that are actually SMALLER. I have no idea where they got that "ten times bigger" value... they say it's an average, but even so. An average of what? All Eukaryotic cells? Metazoan cells? Metazoan + plant cells? I would think that if you'd include Fungi in that, you'd end up with a much larger number.
the cell size of eukaryotes are 10-100um
prokayotes size 1-10um
i believe this is where they got the relationship of being ten times larger
Some Eukaryotic cells are MUCH bigger than 100µm. Acetabularia sp. immediately comes to mind. Not sure how big it is... maybe 5-10cm.
Some Prokaryotic cells are also much bigger than 10µm. Thiomargarita namibiensis can reach 750µm.
I'm wondering where they got the values that you cited, because it's really easy to find both Prokaryotic and Eukaryotic cells outside those size ranges.
im just comparing the smallest cell size of both eukaryotes and prokaryotes
The smallest Eukaryotes can be pretty tiny. Most are not as small as the average bacterium, sure, but Microsporidia can be 1-4µm. That's definitely within the "typical" Prokaryotic range that you gave above.