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 = 
<gadget id="calculator">5*.45</gadget>
<output>2.25</output>
2.25 inches.
He is left with 5 - 2.25 = 
<gadget id="calculator">5-2.25</gadget>
<output>2.75</output>
2.75 inches of chalk.
The next day he will use 20% of 2.75 inches, which is 2.75 * .2 = 
<gadget id="calculator">2.75*.2</gadget>
<output>0.55</output>
.55 inches of chalk used.
That leaves him with 2.75 - .55 = 
<gadget id="calculator">2.75-.55</gadget>
<output>2.2</output>
2.2 inches of chalk.
The day after that, he will use 2.2 * .2 = 
<gadget id="calculator">2.2*.2</gadget>
<output>0.44</output>
.44 inches of chalk.
That will leave him with 2.2 - .44 = 
<gadget id="calculator">2.2-.44</gadget>
<output>1.76</output>
1.76 inches of chalk.
Since 1.76 is less than 2 inches, he will recycle this stick in 2 days.

<result>2</result>