how many possible 3 digit numbers are there that have a middle zero? how many possible 4 digit numbers are there that have two middle zeros? Explain your answears
0- 900 = 90 x 100 = 9000
idk idk
Well, let's take this step by step.
For the first question, we need to find the number of three-digit numbers that have a middle zero. Since we know the middle digit needs to be zero, we have one fixed digit already. The first and third digits can be any number from 0 to 9, giving us 10 options for each digit. Therefore, the total number of three-digit numbers with a middle zero is 10 possible numbers.
Now, for the second question, we need to find the number of four-digit numbers that have two middle zeros. Again, we have two fixed digits already, the two zeros in the middle. For the first and last digits, they can be any number from 1 to 9 since leading zeros are not allowed in a four-digit number. So we have 9 options for each of those digits. Therefore, the total number of four-digit numbers with two middle zeros is 9 possible numbers.
To summarize:
- The number of three-digit numbers with a middle zero is 10.
- The number of four-digit numbers with two middle zeros is 9.
To find the number of possible 3-digit numbers that have a middle zero, we need to consider the possible values for the first and third digits. The second digit is fixed as zero.
For the first digit, it can be any number between 1 and 9, since leading zeros are not allowed in a 3-digit number. Therefore, there are 9 choices for the first digit.
For the third digit, it can also have any value from 1 to 9, since trailing zeros are allowed. Hence, there are 9 choices for the third digit.
To find the total number of possible 3-digit numbers with a middle zero, we multiply these choices together: 9 (choices for the first digit) multiplied by 1 (choice for the second digit, which is fixed as zero) multiplied by 9 (choices for the third digit).
So, the total number of possible 3-digit numbers with a middle zero is 9 x 1 x 9 = 81.
Now, let's move on to finding the number of possible 4-digit numbers that have two middle zeros. In this case, the first and fourth digits can take any value between 1 and 9, while the two middle digits are fixed as zeros.
Similar to the 3-digit case, the first and fourth digits have 9 choices each. The two middle digits, being zeros, do not give us any choices.
To find the total number of possible 4-digit numbers with two middle zeros, we multiply the choices together: 9 (choices for the first digit) multiplied by 1 (choice for the second digit, which is fixed as zero) multiplied by 1 (choice for the third digit, also zero) multiplied by 9 (choices for the fourth digit).
So, the total number of possible 4-digit numbers with two middle zeros is 9 x 1 x 1 x 9 = 81.
In the first case, you are free to choose only the first and lat digits. The first digit must start with 1 and there are 9 of them. The last digit can start with any number 0 to 9, and there are 10 of them. That makes the number of possibilities 9x10 = 90
Try your own hand at the second one. There are a lot of similarities with the first.