Two different 6-digit numbers each have three 8's and and three 7's.No two digits next to each other are the same.write the numbers in standard form
To write two different 6-digit numbers with three 8's and three 7's, while ensuring that no two adjacent digits are the same, we can follow these steps:
Step 1: Determine the positions of the 8's and 7's in the number.
Since we need to have three 8's and three 7's, we can choose any three positions out of the six total positions for the 8's and then fill in the remaining three positions with the 7's.
For example, one arrangement could be:
8 _ _ 8 _ _
Step 2: Fill in the remaining positions with the other digits (non-8's and non-7's).
Since no two adjacent digits can be the same, we cannot place another 8 or 7 next to an existing 8 or 7. Therefore, we need to use the remaining digits (1, 2, 3, 4, 5, 6, and 9) to fill in the remaining positions.
For the first number, fill in the remaining positions with any combination of the remaining digits where no two adjacent digits are the same. For example:
8 1 2 8 3 6
For the second number, follow the same rules to fill in the remaining positions:
8 9 4 8 5 7
Step 3: Write the numbers in standard form.
The standard form of a number is written by adding up the value of each digit based on its position. For a 6-digit number like this, we can determine the value of each position using powers of 10.
For the first number:
8 1 2 8 3 6
8 is in the hundred thousands place= 8 x 100,000 = 800,000
1 is in the ten thousands place= 1 x 10,000 = 10,000
2 is in the thousands place= 2 x 1,000 = 2,000
8 is in the hundreds place= 8 x 100 = 800
3 is in the tens place= 3 x 10 = 30
6 is in the ones place= 6
So, the first number in standard form is 800,000 + 10,000 + 2,000 + 800 + 30 + 6 = 813,836.
For the second number:
8 9 4 8 5 7
8 is in the hundred thousands place= 8 x 100,000 = 800,000
9 is in the ten thousands place= 9 x 10,000 = 90,000
4 is in the thousands place= 4 x 1,000 = 4,000
8 is in the hundreds place= 8 x 100 = 800
5 is in the tens place= 5 x 10 = 50
7 is in the ones place= 7
So, the second number in standard form is 800,000 + 90,000 + 4,000 + 800 + 50 + 7 = 895,857.
Therefore, the two different 6-digit numbers with three 8's and three 7's in standard form are 813,836 and 895,857.