A young couple finds and rents just the apartment they had been looking for. Everything about it seems perfect: size, location and rent they can afford.

One night a few months later they leave the apartment for dinner and a movie. They also leave the gas burner on beneath the teapot. As they turn onto their street several hours later, the fire engines are just leaving.

Everything is lost: clothing, furniture, jewelry, stereo, TV, video recorder.

The worst is yet to come. Their landlord has insurance on the building, which can be repaired, but they did not have insurance on their belongings.

"A common misconception by tenants," says Robert Hunter of the National Insurance Consumers Organization in Alexandria, "is that if their landlord has coverage, they also are automatically covered. Not true."

Landlords typically carry coverage on their rental property much the way homeowners have insurance on their homes. Personal possessions inside the structures are not always covered automatically.

A survey by the Insurance Information Institute shows that only 29 percent of renters have insurance protection of any kind. The breakdown: 26.6 percent had coverage including fire damage to house or contents, 9.8 percent had coverage including flood damage, and 25.2 percent had coverage for theft of personal possessions; 7 percent didn't know whether they had any coverage.

"Unless the damage to a tenant's personal possessions is caused by the landlord's negligence," says Hunter, "uninsured tenants can't collect."

The ounce of prevention, say insurance experts, is simple and relatively inexpensive: Buy a renter's insurance policy (it's called Tenants Form HO-4) covering furnishings and other personal property.

HO-4 policies cover most situations, with only a few exceptions: nuclear war, nuclear accidents and "acts of God." They often include liability coverage (usually $100,000), which would pay for damages and legal fees arising from injuries caused by you or a member of your family (even by pets) on or near your residence -- someone tripping over an extension cord, bites by the family pet.

Tenant's policies also usually cover "loss of use": room, board and other living expenses incurred in the event you have to live away from the rental property while it is repaired, for example.

The cost for such a policy in the Washington area ($15,000 basic coverage, plus $100,000 liability, plus "loss of use") likely would run from $55 to $100 per year, depending on where you are renting and whether you want actual-cash-value or replacement-cost coverage.

The standard HO-4 policy usually offers only limited coverage on loss of such items as jewelry, furs, silver and other valuables. Valuables exceeding the limited coverage can be added, for an additional premium, to the basic policy or under a separate policy.

Homeowners and renters both, say the experts, should make a complete inventory of their personal possessions, with documentation, and store it in a safe place -- a safe deposit box, for example, where it won't be destroyed if there's a fire or other household catastrophe.

Most tenants tend to underinsure, Hunter says. "It's contrary to what we find with most insurance. Single people often buy life insurance, which they don't need." His organization recommends that they put their money instead into tenant's and disability policies.

In terms of shopping for insurance, Hunter asserts that "the companies with the best prices also tend to have the best service. It's sort of the reverse of the adage, 'You get what you pay for.' In insurance, it seems to be the opposite."

Two pamphlets, "Taking Inventory" and "Tenant Insurance Basics," are available free from the Institute, 110 William St., New York, N.Y. 10038, or by calling the institute's toll-free hot line, (800) 221-4954.