Converting (1/2) into a decimal is equal to 0.5, which is a finite decimal; converting (1/11) into a decimal is equal to 0.090..., abbreviated as 0.{_{0}**(•)}{_{9}** (•)} is a pure recurring decimal; converting (1/6) into a decimal is equal to 0.1666..., abbreviated as 0.1{_{6}**(•)}, which is a mixed recurring decimal. Now convert 2004 fractions (1/2), (1/3), (1/4), ..., (1/2005) into decimals, ask: How many pure recurring decimals are there?
将(1/2)化成小数等于0.5，是个有限小数；将(1/11)化成小数等于0.090…，简记为0.{_{0}**(•)}{_{9}**(•)}，是纯循环小数；将(1/6)化成小数等于0.1666…，简记为0.1{_{6}**(•)}，是混循环小数．现在将2004个分数(1/2)，(1/3)，(1/4)，…，(1/2005)化成小数，问：其中纯循环小数有多少个？
<gadget id="calculator">2_004 / 2</gadget>
<output>1_002</output>

<gadget id="calculator">2_005 / 5</gadget>
<output>401</output>

<gadget id="calculator">2_004 - 1_002 - 401</gadget>
<output>601</output>

<gadget id="calculator">2_000 / 10</gadget>
<output>200</output>

<gadget id="calculator">601 + 200</gadget>
<output>801</output>

<result>801</result>