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The display of a 24-hour digital clock shows hours and minutes in the format XX:XX. For what fraction of a day is at least one 0 displayed on this clock?

 Oct 16, 2020
 #1
avatar+10324 
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The display of a 24-hour digital clock shows hours and minutes in the format XX:XX. For what fraction of a day is at least one 0 displayed on this clock?

 

Hello Guest!

 

01h to 10h and 20h              11 x 60min    \(=660\ min\)

11h to 19h and 21h to 24h  13 x (12 + 9)  \(=\underline{273\ min}\)

                                                                  \(=933\ min\)

 24h x 60min/h                                         \(= 1440\ min\)

                                                  \(\frac{933\ min}{1440\ min}=0.648\)


A zero is displayed on 0.648 of a day.

laugh  !

 
 Oct 16, 2020
edited by asinus  Oct 16, 2020
 #2
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0

60 * 12 = 720

 

15 * 12 = 180

 

900 / 1440 = 0.625   or   5/8

 
 Oct 16, 2020
 #3
avatar+27695 
+1

Hmmmm...I get a slightly different answer

 

Each of the hours  00-10   and 20 have a zero the entire 60 minutes   (at 24:00 the clock turns to 00:00)

                                              12 x 60

 

There are 12 hours  (11 -19  and 21,22,23)  left that have zeroes for minutes  00 - 10     and :20  :30  :40  :50  

                                                  12 x 15     (Note: there is no 24:00  ..... at 23:59:59  the next time is 00:00:00)

 

there are 24 x 60 minutes per day

 

(12*60 + 12*15) / (24*60)  * 100% = 62.5 %     as 'Guest ' found

 
 Oct 16, 2020

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