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?

CalculatorUser
Oct 14, 2018

#1**0 **

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!.

Guest Oct 14, 2018

edited by
Guest
Oct 14, 2018

#3**+2 **

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 !!!

CPhill
Oct 14, 2018