A teacher uses a 5-inch piece of chalk to write math equations on a chalkboard for his students. The teacher likes to conserve chalk, so he tries to only use 20% of the chalk each day. Since the teacher cannot write with a very small piece of chalk, he recycles the chalk when it is smaller than 2 inches. On Monday the teacher used a new piece of chalk. His students need extra help that day, so he ended up writing more than usual. He used up 45% of the chalk by the end of the day. If the teacher goes back to using only 20% of the chalk each day, how many days does he have before he has to recycle this piece?
The teacher uses 45% of his 5 inch stick of chalk on Monday, or 5 * .45 = <<5*.45=2.25>>2.25 inches.
He is left with 5 - 2.25 = <<5-2.25=2.75>>2.75 inches of chalk.
The next day he will use 20% of 2.75 inches, which is 2.75 * .2 = <<2.75*.2=.55>>.55 inches of chalk used.
That leaves him with 2.75 - .55 = <<2.75-.55=2.2>>2.2 inches of chalk.
The day after that, he will use 2.2 * .2 = <<2.2*.2=.44>>.44 inches of chalk.
That will leave him with 2.2 - .44 = <<2.2-.44=1.76>>1.76 inches of chalk.
Since 1.76 is less than 2 inches, he will recycle this stick in 2 days.
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