GOV. CHARLIE BAKER sported a mask on Saturday while taking a tour of a mask-cleaning facility in Somerville and said one of the reasons why he and his administration have embraced face-coverings is because a significant number of people are walking around as COVID-19 carriers and don’t know it.

“There’s a growing consensus about this particular virus that there is a significant, a minority population but a significant portion of the population, who are not going to show symptoms. They will be infected, they are carriers, but they are not going to show symptoms,” Baker said.

Baker said estimates of the size of the population of invisible carriers run from 20 to 40 percent; an aide said later the percentage was of the total infected population. He said the exact number is almost impossible to figure out until a lot more COVID-19 testing is conducted.

The governor said part of the reason his administration put out the new guidance on masks on Friday is to protect people from others who are walking around infected and don’t know it – and to protect others from the mask wearer if he or she is infected and doesn’t know it.

Baker didn’t address the serious problem this infected-but-not-showing symptoms issue raises for all sorts of government agencies and businesses that interact regularly with people. At the MBTA, for example, the temperature of workers is taken when they arrive for work and those with fevers are sent home. But if an infected person doesn’t exhibit a fever they would be allowed to work.

Similar problems exist at nursing homes, which are emerging as the top COVID-19 hotspot in the state. Employees at nursing homes may be infected and not know it. Even if they are extremely careful, the employees could be passing along the disease to residents who are extremely vulnerable. Nursing home industry officials say their business revolves around the personal care of elderly patients, the type of work that is just the opposite of social distancing.

According to figures released on Saturday, 304 people have died from COVID-19 at nursing homes, rest homes, and skilled nursing facilities. That number was up 24 percent from the first nursing home fatality number issued on Friday.

Statewide, the death toll from COVID-19 is now at 686, up 87 from Friday. Nursing home fatalities represent 45 percent of the total statewide deaths and they represented 68 percent of the increase statewide on Saturday.

Since the nursing home death toll was first released on Friday, the Baker administration has announced no new policies or strategies to address the situation other than increased testing by a team of 250 members of the National Guard.

Baker made his comments after taking a tour of a facility in Somerville set up to disinfect up to 80,000 masks a day. The service will be free to local hospitals for now because of a contract the federal government negotiated with Battelle to set up similar facilities across the country. Baker pointed out that when the federal grant money runs out, hospitals will pay $3.50 per mask, which is basically the price of a new mask. The disinfecting facility allows the same mask to be used safely up to 20 times.