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# clock problem

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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

#1
+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
+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) = ............

Guest Jan 5, 2021
#2
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
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