Terrence Williams would go grocery shopping but decide against getting too many of one thing because he didn’t know if he’d be in Boston long enough to need it.

After all, the swingman was only on a 10-day contract with the Celtics, a pact that was set to expire Friday night.

But Williams can settle down for a bit and buy in bulk if he so chooses after the Celtics signed him for the remainder of this season Friday, along with a conditional deal for the 2013-14 season.

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“It eases a lot of pressure, but at the same time, you don’t want to be too relaxed, because there’s a reason why they signed you, and it’s definitely for your personality and your basketball skills,” Williams said before the Celtics beat Golden State, 94-86.

Instead of signing Williams to another 10-day contract, the team chose to lock up the former lottery pick to an extended deal.

“I like the way he’s played, minus one game,” coach Doc Rivers said, alluding to Williams’s subpar performance Feb. 24 at Portland when Williams played seven erratic minutes, missing three of four shots.

“And now that he’s going to be here, we have a chance, hopefully, to turn him into a player that we think he could be.”

What type of player would that be?

A point guard.

Though the 6-foot-6-inch Williams may be oversized for that position, his playmaking skills and court vision make the Celtics believe that’s the spot for him.

The Celtics first developed that belief when Williams worked out for them last summer.

“Just pickup games and just watching the way he played, you really felt that even in those situations that he’s more point than [shooting guard],” Rivers said.

“I don’t think he’s ever going to be a great scorer in our league, but he can be a great playmaker.”

Entering Friday, Williams was averaging 4.3 points and 2.0 assists in 14.7 minutes. He then played an uneventful minute in the win.

Well-traveled trio

The Chinese Basketball Association has become a sort of farm league for the shorthanded Celtics, who have added three former NBA players who were playing there.

Shavlik Randolph became the third Friday. The former Duke star signed a 10-day contract.

Randolph, a 6-10 forward, played in 28 games for the Foshan Long Lions this season, averaging 32 points and 14.6 rebounds.

Randolph averaged 2.4 points and 2.4 rebounds over 95 NBA games spread across five seasons split among Philadelphia, Miami, and Portland. He last played in the NBA in the 2009-10 season.

Williams and D.J. White, who is on a 10-day contract, also played in China.

“We were going through shootaround this morning, it was me, Terrence, and D.J., and I was just like, ‘Man, this is a CBA team right here,’ ” Randolph said.

“It definitely makes us more comfortable, just been playing with these guys and against them. I think it helps all of us in this situation.”

Randolph said he hasn’t discussed his role with Rivers.

“If I go in there, to hustle, to try to rebound, try to play defense, take charges — not get fined for flopping,” he said. “That’s kind of always been my role on any team I’ve been with. If I’m open, make open jump shots. I kind of know that’s what my role is.”

The Celtics have added players at midseason before, but Rivers said this is different because these players are young.

“A lot them really haven’t established themselves as players yet, where in the past, the P.J. Browns and the Gary Paytons or whoever else we brought in had pretty much established themselves,” Rivers said. “You knew who they were and I thought those [situations] were easier.”

When asked if he felt comfortable putting the new players on the court, Rivers made it clear that the additions are fill-ins, nothing more.

“I’m not bringing guys in to take any of those other guys’ spots,” he said. “So, obviously if one of them comes in and helps us, that’s good, but that’s their role, to be ready to play and be ready to not play and to understand what we’re doing.”

Melo to Maine

The Celtics reassigned rookie center Fab Melo to the Maine Red Claws of the D-League . . . Rivers was nominated for Eastern Conference Coach of the Month for February, but lost to Miami’s Erik Spoelstra. The Celtics went 8-4 last month and Miami went 12-1.