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A digital, 12-hour clock shows hours and minutes. During what fraction of the day will the clock show the digit 0 in its display? Express your answer as a common fraction.

 Jan 5, 2021

Best Answer 

 #1
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+1

For each hour    100 200 300

   there are 2 zeroes   + 1 extra at 1000   = 25 zero minutes

     each hour has a 10 20 30 40 50 after      12 x 5 = 60 more zero showing minutes

       each hour has a  01 02 03 04 05 06 07 08 09     12 x 9 = 108 zero-minute hours

        ALL of the munutes during 1000 hour have zero    54 more minutes (because the 10 20 30.... were already counted )

 

(25+60+108 + 54 )  / (12*60) = ............

 Jan 5, 2021
 #1
avatar
+1
Best Answer

For each hour    100 200 300

   there are 2 zeroes   + 1 extra at 1000   = 25 zero minutes

     each hour has a 10 20 30 40 50 after      12 x 5 = 60 more zero showing minutes

       each hour has a  01 02 03 04 05 06 07 08 09     12 x 9 = 108 zero-minute hours

        ALL of the munutes during 1000 hour have zero    54 more minutes (because the 10 20 30.... were already counted )

 

(25+60+108 + 54 )  / (12*60) = ............

Guest Jan 5, 2021
 #2
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0

(note that his is a 12 hour clock.....so it will do this twice a day.....and the denominator will be twice as big....so we can calc just for one of the  12 hour cycles)

Guest Jan 5, 2021
 #3
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0

* * * edit * * *

 

  45 more minutes (because the 10 20 30.... were already counted   as were 01 02 03..... )

(25+60+108 + 45 )  / (12*60) = ............

Guest Jan 5, 2021

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