To round the number 6.141359 to the nearest ten-thousandth, we need to look at the fifth decimal place, which is the number in the ten-thousandths place.
The number 6.141359 can be broken down as follows:
- The digit in the ten-thousandths place (the fourth decimal place) is 3.
- The digit in the hundred-thousandths place (the fifth decimal place) is 5.
Since the digit in the hundred-thousandths place (5) is 5 or greater, we round up the digit in the ten-thousandths place (3) by one.
Therefore, rounding 6.141359 to the nearest ten-thousandth gives us 6.1414.