If you're working with voltages, a 50% reduction/gain is 6 dB, not 3 dB.
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An 8 way splitter means 35db / 8 = 4db.
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Nope. It's closer to 3.5*3. Typical insertion loss is around 3.5 per split, I've tested anywhere from 3.2 to 4.4 dB insertion loss in 2 port splitters. An 8-port splitter usually has around 10.5 dB insertion loss. More or less, depending on the device's efficiency at the frequency tested or specified. If you use a nominal value of 3.5-4.0 dB per half split, you'll stay close enough to keep out of trouble.
If you allow for 11 dB for an 8 port splitter in your distribution link budget, you'll be okay.