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Bangladesh were batting at 182 for none in 33.2 overs when the rain halted the play.
The match has now been reduced to a 43-over a side.
Liton Das hit a century right before the rain hit the game. It was his second century in the series. He was not out for 102* before the rain while Tamim Iqbal was unbeaten for 79*.
Along the way, Liton and Tamim made the record of scoring highest opening stand for the Tigers in ODIs. They surpassed the previous record of the highest runs in the opening stand of 170 made by Shahriar Hossain and Mehrab Hossain in 1999 against the same opponent.
Earlier, Zimbabwe won the toss and opted to bat first in the match which will be marked as Bangladesh’s last match under the captaincy of Mashrafe Bin Mortaza.
Before this game, Mashrafe led the Tigers in 87 ODIs and won 49 of those. If Bangladesh win this game, Mashrafe will be the first Bangladeshi captain to enjoy 50 wins in a single format of international cricket.