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If you're using potassium permanganate, you'll need the potassium permanganate crystals, cotton swabs, and a bit of water to moisten the swabs. Potassium permanganate is a powder made up of bright purple crystals and is the preferred method of veterinarians to stop bleeding nails. It's highly effective and the permanganate is a natural disinfectant. Potassium permanganate crystals are widely available on internet retail sites. Ideally you've anticipated this scenario and can calmly use the materials you've prepared to stop the bleeding. The blood loss from a bleeding nail is not dangerous to a healthy dog. The bleeding nail can, however, look a bit dramatic, especially if the dog scrambles around spreading blood all over the floor. Know that the dog is in no danger, but act quickly to minimize its discomfort. Remember that remaining calm is important for you but also for your dog. The quick is tender and full of nerves, so having it clipped will be painful to your dog and it will be looking to you for cues on how to react. If you get panicked or frantic, your dog likely will, too. It's important that the swab be slightly moist so that the potassium permanganate crystals will adhere to it. You don't need to soak the swab, just dampen it with a few drops of water. The crystals should stick to the moistened swab. Dip the end of the moistened swab into the potassium permanganate 1 time. Gently restrain your dog while you apply the swab. The bleeding should stop fairly quickly. If the bleeding hasn't stopped, repeat the above process again, this time holding the swab in place for 5 minutes. If after 5 minutes the bleeding still hasn't stopped, contact your vet.

Summary:
Get your supplies ready. Stay calm. Moisten the tip of a cotton swab with water. Dip the moistened cotton swab in the potassium permanganate. Press the swab into the bleeding quick and hold for 30 seconds. Repeat.