To determine which of the numbers 6.399 or 6.400 is larger, we can compare the digits in each place value from left to right:
- Looking at the ones place: Both numbers have "6" in the ones place, so they are equal in this place.
- Moving to the tenths place: Both numbers have "3" in the tenths place, so they are also equal in this place.
- Next, we look at the hundredths place: Both numbers have "9" in the hundredths place, so they are still equal in this place.
- Finally, we compare the thousandths place: In 6.399, the thousandths place is "9," while in 6.400, the thousandths place is "0."
Since 9 (in 6.399) is greater than 0 (in 6.400), this means that 6.399 is greater than 6.400.
Thus, the thousandths place is the first place value that determines that 6.399 is larger than 6.400.