Final answer:
To round the decimal 0.074966 to the nearest ten-thousandth, we look at the digit right after the ten-thousandth place, which is the hundred-thousandth place. If this digit is 5 or greater, we round up the ten-thousandth place. If it is less than 5, we round down the ten-thousandth place. In this case, we round up the ten-thousandth place to get 0.075.
Step-by-step explanation:
To round the decimal 0.074966 to the nearest ten-thousandth, we need to look at the digit right after the ten-thousandth place, which is the hundred-thousandth place. If this digit is 5 or greater, we round up the ten-thousandth place. If it is less than 5, we round down the ten-thousandth place. In this case, the digit in the hundred-thousandth place is 6, which is greater than 5. So, we round up the ten-thousandth place. The rounded decimal is 0.075.