A number has 4 digits. The digit in the hundredths place us greater than the digit in the hundredths place of 4.361. The digit in the tousandths 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?
To find the possible four-digit numbers between 8.6 and 8.7, we need to determine the possible values for each decimal place.
Given that the digit in the hundredths place is greater than the digit in the hundredths place of 4.361, we know that the number has to be greater than 4.361. So the hundredths place digit can be either 4, 5, 6, 7, 8, or 9.
The digit in the thousandths place is greater than the digit in the tenths place of 2.85. The tenths place digit of 2.85 is 5, so the thousandths place digit can be any number from 6 to 9.
Combining the possible values for each decimal place, we can construct the possible four-digit numbers between 8.6 and 8.7.
Starting with the hundredths place:
- If the hundredths place digit is 4, the remaining digits can be any numbers from 7 to 9 in the thousandths, tenths, and units places.
- If the hundredths place digit is 5, the remaining digits can be any numbers from 6 to 9 in the thousandths, tenths, and units places.
- If the hundredths place digit is 6, the remaining digits can be any numbers from 0 to 9 in the thousandths place, any number from 0 to 7 in the tenths place, and any number from 0 to 9 in the units place.
- If the hundredths place digit is 7, the remaining digits can be any numbers from 0 to 9 in the thousandths place, any number from 0 to 5 in the tenths place, and any number from 0 to 9 in the units place.
- If the hundredths place digit is 8, the remaining digits can be any numbers from 0 to 9 in the thousandths place, any number from 0 to 6 in the tenths place, and any number from 0 to 9 in the units place.
- If the hundredths place digit is 9, the remaining digits can be any numbers from 0 to 9 in the thousandths place, any number from 0 to 7 in the tenths place, and any number from 0 to 9 in the units place.
By combining the possible values for each decimal place, we can create the following list of four-digit numbers between 8.6 and 8.7:
- 8.647
- 8.657
- 8.660
- 8.661
- 8.662
- 8.663
- 8.664
- 8.665
- 8.666
- 8.667
- 8.668
- 8.669