What is the probability that a randomly selected three-digit number is divisible by 11? Express your answer as a common fraction.
makes no sense
To find the probability that a randomly selected three-digit number is divisible by 11, we need to determine how many three-digit numbers are divisible by 11 and then divide that by the total number of three-digit numbers.
To determine how many three-digit numbers are divisible by 11, we need to find the difference between the largest and smallest three-digit numbers divisible by 11 and add 1.
The smallest three-digit number divisible by 11 is 110, and the largest is 990. We can find these by finding the smallest multiple of 11 that is greater than or equal to 100 (11 * 10 = 110) and the largest multiple of 11 that is less than or equal to 999 (11 * 90 = 990).
So, there are (990 - 110 + 1) = 881 three-digit numbers divisible by 11.
The total number of three-digit numbers is calculated by subtracting the smallest three-digit number (100) from the largest three-digit number (999) and adding 1.
So, there are (999 - 100 + 1) = 900 three-digit numbers in total.
Therefore, the probability that a randomly selected three-digit number is divisible by 11 is 881/900, which can be simplified to 97/100.
(999-99)/11 = 81.81
so, there must be 81 multiples of 11 between 100 and 999
99+81*11 = 990
99+82*11 = 1001