each 100 ms....The frequency range will be from 10.83 HZ to 141.6 HZ.
Let's forget Arduino and any particular Arduino library for a minute.
If you want to use a simple frequency counter to measure frequency to the nearest tenth of a Hz, you will have to have a "gate" that is opened to the counter for ten seconds. Then the counter is reset, the "gate" is opened for ten seconds so that the counter can increment on each positive transition of the input signal and then the gate is closed. (You could use negative transitions instead of positive; the principle is the same).
After you close the "gate," if you divide the count value by 10.0, giving a floating point result, you have the frequency to the nearest 0.1 Hz (plus or minus a least-significant bit).
If you want to measure the frequency approximately every 100 ms, the "gate" duration could be 100 ms (0.1 seconds), and the count value at the end of the gate time would be the frequency in tens of Hz. That is, you get the frequency in Hz by multiplying the count value by 10 (so the least significant decimal digit of the Hz value would always be zero). This, obviously wouldn't meet your requirements.
To measure low frequency signals every 100 ms with simple circuitry, you could measure the period between positive transitions, not the count value for a gate time of 100 ms.
Suppose we can measure the time between two positive transitions in microseconds. Then the frequency in Hz would be 1000000.0 / (period in microseconds)
Now, back to Arduino stuff...
Here's my take on it: The frequency counter library doesn't seem appropriate for measuring the frequency of a 10 Hz signal, accurate to the nearest tenth of a Hz every 100 ms. In fact, as far as direct measurement of frequency to the nearest tenth of a Hz with a gate time of 100 ms, well...I might be tempted to make a rare (for me) flat statement: No Way!
On the other hand it is definitely possible to measure, in microseconds, the time between two positive transitions of a signal. Whether you can make such measurements (with an Arduino) with sufficient accuracy over your desired range of frequencies is another thing. I haven't tried it, but maybe others can report on actual experience
measuring periods of low frequency signals. Note that measuring the period might be very appropriate for frequencies of a few tens of Hz, but not necessarily for frequencies of a few hundreds of Hz (or more).
Consider the following:
The difference in periods between 10.1 Hz and 10.2 Hz is something around 9800 microseconds. In order to report frequencies this low to the nearest tenth of a Hz, you have to measure the period with an accuracy of something like plus or minus 4900 microseconds, and that's something that I think you could manage with an Arduino with no real problems. For that matter, if you can measure period plus or minus 50 microseconds, you can calculate the frequency of signals with frequencies near 10 Hz to the nearest hundredth of a Hz.
The difference in periods between 100.1 Hz and 100.2 Hz is something like 10 microseconds. It might take some work to satisfy yourself that you can measure the period with an accuracy of plus or minus five microseconds, but, maybe, just maybe, it's not impossible.
On the other hand...
The difference in periods between 1000.1 Hz and 1000.2 Hz is something like 0.1 microseconds, and I see no hope in measuring this directly in software.
Here's the bottom line as I see it:
Measuring the frequency (in software) directly to the nearest tenth of a Hz requires a gate time of 10 seconds, not 100 milliseconds.
Measuring the period (in software) in microseconds so that frequency can be calculated to the nearest tenth of a Hz doesn't seem practical for frequencies much higher than 100 Hz, but I won't rule it out as an absolute impossibility. (For 141 Hz, to get results plus or minus a tenth of a Hz, you would have to measure period plus or minus 2 microseconds. That's a real challenge, I'm thinking.)
Perhaps an "RPM Module" based on a 2907/2917 chip might be the way to go. I haven't used any such chips, so I don't know how easy it is to get accurate results. I mean, I would rather do things "all-digital" but...
Finally, note that:
"Real" frequency counters use combinations of hardware dividers and phase-lock loops and other hardware and/or software "tricks" to be able to display results for a wide range of frequencies of periodic signals.