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Apple's claimed battery life on this iPod is 10 hours. That's two hours less than the previous Shuffles.
The 3.7 volt lithium-polymer battery lists a capacity of 0.27 watt-hours.
To calculate the capacity in amp-hours, we know P(power) = I(amps)*V(volts), so I = P/V. That yields a capacity of about .073 amp-hours, or 73 mAh. That's definitely record-breakingly small in terms of iPod batteries.