select a capacitor as a filter for a battery pack

Are you using the capacitor to suppress RF?  That's about the only reason to put caps across a battery pack.  I personally don't see the need for it because the battery doesn't care about incoming RF and it doesn't generate any either ... but you pays your money and you takes your choice.

In the case of a battery pack powering a small amplifier there's no need for a hash suppression cap.  There's no loss by installing one, but it won't do anything useful.  Nor will a filter cap, because the DC is clean.

Where this would be useful is if there is a power jack in parallel with the battery pack.  In that case yes, both a filter cap and an RF suppression cap are useful because so many wall warts produce not-very-good DC and free RF hash to boot.

In that case the standard value for RF suppression would be .001 uF = 1 nF.

A battery by itself is a HUGE capacitator

Batteries are not capacitors, and you can't use them as such.  Batteries are power sources.  They have different chemistries and are used for different purposes.  You can't cycle batteries at high frequencies and not all batteries can be recharged properly.

You mainly need a filter capacitor to keep input voltages safe for charging, in case the voltage fluctuates too much.  It fully depends on what kind of circuit you have.
https://www.elprocus.com/what-is-a-filter-capacitor-working-and-its-applications/

In power supply circuits, this capacitor can be calculated to ensure the least ripple at the output. The formula is C = I / 2f Vpp

From the equation above, ‘I’ is load current, ‘f’ is i/p frequency of AC and ‘Vpp’ is the minimum ripple that may be acceptable because almost it’s never possible to make this ‘0’

Thanks for all that feedback.  What I was taught when I was in school was that a battery is not a perfect source, only a zener controlled PS was a close to perfect source.   A battery may be a fine PS for a flashlight, but the chemistry of the battery can be heard in an audio application as small/light cracking and popping noise. sometimes confused w/RF noise.
Is all that stuff wrong ?
 

the chemistry of the battery can be heard in an audio application as small/light cracking and popping noise. sometimes confused w/RF noise. complete and utter bull pucky

battery is not a perfect source, only a Zener controlled PS was a close to perfect source Different chemical batteries have different discharge curves i.e. Alkaline/zinc batteries are 1.5V and over the discharge cycle drop.. NiCad's otoh are 1.25V and maintain this and will drop to 0V without dropping in voltage.

Below is a basic rough guideline of capacitors that can be used for various frequencies.
For coupling a 100Hz signal, a 10μF capacitor can be used.
For a 1000Hz signal, a 1μF capacitor can be used.
For a 10KHz signal, a 100nF capacitor can be used.
For a 100KHz signal, 10nF capacitor can be used.
For a 1MHz signal, a 1nF capacitor can be used.
For a 10MHz signal, a 100pF capacitor can be used.
For a 100MHz signal, a 10pF capacitor can be used.

This is a rough estimate that will be effective the majority of the time. The only variable that could affect the above values is the resistance in parallel to the capacitor. If the resistance in parallel to the capacitor is about 10K‎Ω or less, all the values will hold true. Usually the resistance is much less than this amount. However, if the resistance is greater, such as between 10K‎Ω and 100K‎Ω, you can divide the above capacitor by 10; meaning you can use even a smaller capacitor. It's perfectly fine if you use the capacitor above, the coupling will work just as well. But you could use even a smaller capacitor, because if the resistance in parallel is larger, that makes the AC signal choose the capacitor path that much easier than the resistor path, because the capacitor path has much less resistance compared to the resistor if the resistor is larger. So as the resistance increases, the capacitance value can decrease. But, again, using a larger capacitor value than what is needed could never hurt. Using a smaller capacitor could.

So this is an effective method for choosing the value of a coupling capacitor. It allows for low-frequency or high-frequency coupling.

the main difference between a capacitator and a battery is its charge and discharge rates.  They both store energy.  When I said a battery is like a large capacitator I was thinking in the hundreds or thousands of farads.  I have used capacitators as extremely short duration batteries

If you really must remove almost all noise, then add your zener circuit.

While they both store energy, they're still different things.  There's a reason they have different schematic symbols.  Capacitors will not store the same amount of energy as a battery and a battery might be able to cycle at 1/3600 Hz, making it entirely unsuitable for most capacitor functions.  They're not really interchangeable.

If you really must remove almost all noise, then add your zener circuit.
could you explain to me how a battery pack introduces noise?

When an Zener diode is in the reverse (voltage regulating) condition, it produces impulse noise when it breaks over, plus Zener noise when it is at or over the knee.  This is no solution to noise; it takes relatively clean DC and making it dirty with noise from DC to infinity, requiring a C-L-C pi-network filter to clean it up again.

"In this condition, the diode generates shot noise, which is temperature and frequency independent, in contrast to Johnson-Nyquist noise that is proportional to temperature."

https://www.mpdigest.com/2021/07/23/all-hail-the-zener-diode-noise-source/

I reached out to a former professor and posted my question to him.  His answer was that when building radio circuits the radio frequency can leak back to the batteries and significantly shorten the life of dry-cell batteries.
Most likely that cap is there to shunt these frequencies from leaking back to the batteries.

Thanks