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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 1 in its display? Express your answer as a common fraction.

 

The correct answer is 1/2. But why?

 Oct 14, 2018
 #1
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In the 12 hours of AM, it will show for 1 full hour between 1 AM and 2 AM. So, that is: 1 in 12 hours.

In the 12 hours of  PM, it will show for 1 full hour between 1 PM and 2 PM. So, that is: 1 in 12 hours.

So: 1 + 1 =2 hours in 12 + 12 = 24 hours. Or 2 / 24 = 1 / 12, or 1 in 12 hours, not 1/2 as you have it written.

Note: I'm only counting the HOURS HAND!. The MINUTE HAND will show 16 ones EVERY HOUR!.

 Oct 14, 2018
edited by Guest  Oct 14, 2018
 #2
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That cannot be right!! How about 10, 11, 12 O'clock.......etc.!!!!

 Oct 14, 2018
 #3
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There are  12 * 60   =  720  possible minutes displayed

 

From 10 - 2....  4hrs * 60 mintes per hour   = 240  minutes display  a "1"

 

Every hour between 2 and 10.....the following minutes display at least one "1"

 

10 , 11, 12, 13, 14, 15, 16 ,17 , 18, 19

01, 21, 31, 41, 51

 

So...that's  15 occurrences per hour  * 8 hrs  =  120 additional minutes

 

So...the total number of minutes displaying  at least one "1"  = 240 + 120  = 360

 

So

 

360 / 720    = 1/2    !!!

 

cool cool cool

 Oct 14, 2018
edited by CPhill  Oct 15, 2018
 #4
avatar+2328 
+1

Thank you so much!!! I understand now!

CalculatorUser  Oct 14, 2018

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