how many integer below 100 whose reciprocal are recurring
a)90
b)92
c)85
d)75

• As The fraction will terminate or non-recurring if and only if the denominator has for prime divisors only 2 & 5, that is, if and only if the denominator has the form: 2^n * 5^m
  Possible Combination of No. < 100 of form 2^n * 5^0 = 1,2,4,8,16,32,64
  Possible Combination of No. < 100 of form 2^0 * 5^m = 5,25 ( 1 is already taken)
  Possible Combination of No. < 100 if we relate above two 10(5*2),20(5*4),40(5*8),80(5*16) & 50(25*2)
  So total 14 Numbers possible which can be Non - Recurring
  Thus Ans is (99 - 14 ) = 85 positive Integer below 100 whose reciprocal are Recurring.
• 9 years agoHelpfull: Yes(86) No(1)
• Ans: 85
  non recurring no. are 1,2,4,8,16,32,64 and 5,10,20,40,80, and 25,50..
• 9 years agoHelpfull: Yes(6) No(0)
• 75 substract of all 2 and 5 mutiples 6+19=25 100-25=75
• 9 years agoHelpfull: Yes(3) No(14)
• ALL NON RECURING NUMBERS ARE 2 POWERS 1,2,4,8,16,32,64(TOTAL 7)
  ALL 5 MULTIPLIES 5,10,20,25,40,50,80 (TOTAL 7)
  (REMOVING ALL 3,7,11,13,17,19 MULTIPLES) I.E (15,30,35,45,55,60,65,70,75,85,90,95)
  1/3=0.33333
  1/7=0.14285
  1/11=0.099
  1/13=0.76123076
  SO 99-14=85
• 9 years agoHelpfull: Yes(3) No(0)
• Ans :92
  Check for each numbers remainders when it divides 1.
• 9 years agoHelpfull: Yes(1) No(5)
• Ans:85
  no. are 2,4,6..........
  and 5,10,20......
  and 25,50.....
• 9 years agoHelpfull: Yes(1) No(4)
• As The fraction will terminate or non-recurring if and only if the denominator has for prime divisors only 2 & 5, that is, if and only if
  the denominator has the form: 2^n * 5^m
  
  Possible Combination of No. < 100 of form 2^n * 5^0 = 1,2,4,8,16,32,64
  Possible combination of No.
• 9 years agoHelpfull: Yes(1) No(0)
• reciprocal of all prime no. doesnot give recurring decimal...4 ex. ---1/17=588235294176.....it is not terminated nor recurred ...so how could i consider ds typ of no.
• 8 years agoHelpfull: Yes(1) No(0)
• @reddyl.... but suppose 30.. it is divisible by 5 but 1/30 is recurring decimel... i guess this will be 85
• 9 years agoHelpfull: Yes(0) No(1)
• These numbers 1,5,10,20,25,50,80 wont provide Recurring decimals on reciprocal.
  All the Numbers Xcept these will do..
  So total number less than 100 that will provide recurring decimals after inverse must be
  (99-7) = 92
  I hope this could be helpful.
• 9 years agoHelpfull: Yes(0) No(5)
• I think it should be 86.All non recurring numbers are 1,2,4,5,8,10,16,20,25,32,40,50,64,75.
  I know its not in options but can any1 give example apart from this?
• 9 years agoHelpfull: Yes(0) No(4)