The (International Unit=IU) measurement used to calculate and measure dosages of insulin. Each unit of insulin is expected to have a particular medical effect on the subject.
Full unit(s) can also be described as "even units", meaning there are no fractions (example: 1 1/2--1 1/4) involved. In most adult humans, a difference of 1 full unit is roughly the smallest amount that makes a significant repeatable clinical difference in dosage.
The smaller the patient, the more chance you will need to deal with dosages having fractions in them. An example is found in children, who are smaller and need less insulin than adults; many find the 3/10 syringes with half-unit markings a great help with drawing children's insulin. Cats are normally about 1/10 the body weight of humans and so it's possible for them to react differently to 1/10 of a unit's difference in dosage. Dogs' weight lies along the range between cats and children.
Insulin dosage is often specified (to vets and doctors only) in terms of units/kg body weight. In humans and dogs this is a common way to calculate a rough target dose (though individual cases will differ and dosing should always begin conservatively!). In cats, the current FDMB consensus is that diet and other factors dominate body weight so as to make it inappropriate to base dosing decisions on.
Measurement of insulin in syringes is based on the cubic centimeter (cc) volume measurement system for injectable liquid medications. Your box of syringes is labeled as to how many cc's a syringe will hold. U100 and U40 syringes labeled as 1cc will each hold one cubic centimeter (ml) of liquid, although as the insulin strength is increased, more units will be packed into one cc. A cc (holding a milliliter of liquid) contains 40 Units of U40 insulin, 50 Units of U50 insulin, or 100 Units of U100 insulin.
It is possible, though usually not recommended, to dose U40 insulin in a U100 syringe. Be careful to convert the right way! See this table from felinediabetes.com.
With so many abbreviations, one can sometimes get confused. An easy way to separate units (U) from milliliters (ml) is to think about the following: all commonly-available vials of insulin approved for humans are 10ml vials. Most insulin cartridges contain 3 ml of insulin each. Caninsulin/Vetsulin comes in both a standard 10ml vial and a pack of 10 2.5ml vials. Since a U100 1cc syringe holds 1 milliliter of liquid, drawing this amount from the insulin vial would fill the syringe with 100 units of insulin; that would also be 1/10 of an entire 10ml vial and 1/3 of a 3ml insulin cartridge; it would be more than 1/3 of a 2.5 ml Caninsulin or Vetsulin vial.
If a dosage looks wrong to you, don't be afraid to ask someone for help--your vet, the feline or canine diabetes message boards--before you give an injection of a questionable dose. Delaying a shot if you're not sure is much safer than the alternative.
Insulin Starting Doses
Pounds converted to kilos and rounded down to whole number
Insulin doses based on 0.25-0.50 IU per kilo, rounded down to nearest whole or half unit