a number has four digits. the digit in the hundredth place is greater than the digit in the hundreths place of 4.361. the digit in the thousandths place is greater than the digit in the tenths place of 2.85. what are the possible four-digit numbers between 8.6 and 8.7?

The number is a.bcd

the digit in the hundreths place of 4.361 is 6, so, c>6

the digit in the tenths place of 2.85 is 8, so d>8

a.b = 8.6

So, we have

8.6[789]9
where the 3rd digit can be any of those in brackets.

To find the possible four-digit numbers between 8.6 and 8.7, we need to consider the range of values for each digit based on the given conditions.

In the number 8.6, the digit before the decimal point is 8, which represents the digit in the thousandth place. Since the given condition states that the digit in the thousandth place is greater than the digit in the tenths place of 2.85, the digit in the thousandth place of the four-digit number can be any number from 0 to 8.

The digit after the decimal point in 8.6 is 6, which represents the digit in the hundredth place. The given condition states that the digit in the hundredth place is greater than the digit in the hundredths place of 4.361. Therefore, the digit in the hundredth place of the four-digit number can be any number from 4 to 9.

Now, let's consider the number 8.7. The digit before the decimal point is 8, representing the digit in the thousandth place. Similar to before, the digit in the thousandth place of the four-digit number can range from 0 to 8.

The digit after the decimal point in 8.7 is 7, representing the digit in the hundredth place. According to the given condition, the digit in the hundredth place can be any number from 4 to 9.

Combining all the possible values for each digit, we can conclude that the possible four-digit numbers between 8.6 and 8.7 are:

8.604
8.605
8.606
8.607
8.608
8.614
8.615
...
8.799

Note: There are many possible combinations within this range, so the list of numbers is not exhaustive.