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I suppose Roman numerals would be one counterexample, but are there any number systems based on place/position value that qualify as counterexamples?
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Of course. The Chinese number system is base 10 (or, if you scale way up, base 10,000) with a positional writing system.

The symbol for ten is 十. Heck, there's also a symbol for twenty, 廿, and it exists despite the number system being base 10. Anything that has to be written a lot is likely to have a convenient written form.

If you're curious, zero is 零. Successive zeroes are combined, so 一千零一 is 1001. 5147 would be 五千一百四十七. 10, as previously mentioned, is 十.

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