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# The display of a 24-hour digital clock shows hours and minutes

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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
+10820
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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.

!

Oct 16, 2020
edited by asinus  Oct 16, 2020
#2
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60 * 12 = 720

15 * 12 = 180

900 / 1440 = 0.625   or   5/8

Oct 16, 2020
#3
+28025
+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