How do you determine which digit(s) can be placed in the blank space in the number 3,71_ for it to be divisible by 3?
To determine which digit(s) can be placed in the blank space in the number 3,71_ for it to be divisible by 3, we need to apply the divisibility rule for 3. According to this rule, a number is divisible by 3 if the sum of its digits is divisible by 3.
In this case, the given number is 3,71_, so we need to consider the possible digits that can be placed in the blank space. The sum of the digits 3, 7, 1, and the unknown digit(s) should be divisible by 3 in order for the whole number to be divisible by 3.
Let's calculate the sum of the known digits 3 + 7 + 1 = 11. Now, we can check which digit(s) can be placed in the blank space to make the sum divisible by 3.
To check if a number is divisible by 3, we can simply check if the sum of its digits is divisible by 3. Since 11 is not divisible by 3, we need to find the digit(s) that can be added to 11 to make it divisible by 3.
The possible digits are 0, 2, 4, 5, 6, 8, and 9. We can try adding these digits one by one to the sum until we find a digit that makes the sum divisible by 3.
By adding the digit 4 to the sum 11, we get 11 + 4 = 15. Now, we check if 15 is divisible by 3. Since 15 is divisible by 3, we can conclude that the digit 4 can be placed in the blank space to make the number 3,714 divisible by 3.
Therefore, the digit(s) that can be placed in the blank space in the number 3,71_ for it to be divisible by 3 is 4.