Final answer:
To determine the greatest decimal value, compare the digits from the leftmost non-zero digit. The decimal number 0.1201 has the greatest value because its hundredths place is 2, which is higher than the hundredths place of the other numbers.
Step-by-step explanation:
To determine which decimal number has the greatest value out of 0.1145, 0.1201, 0.1199, and 0.0999, we need to compare each decimal place starting from the leftmost non-zero digit. First compare the tenths place, then the hundredths if necessary, and so on until the difference is found.
- 0.1145 - 1 is in the tenths place, 1 is in the hundredths place.
- 0.1201 - 1 is in the tenths place, 2 is in the hundredths place.
- 0.1199 - 1 is in the tenths place, 1 is in the hundredths place, but 9 is in the thousandths place which is greater than the 4 in 0.1145 and the 0 in 0.1201.
- 0.0999 - 0 is in the tenths place which is less than the 1 in the other numbers.
The decimal number 0.1201 has the greatest value because its hundredths place is 2, which is greater than the hundredths place of the other decimal numbers listed.