Final answer:
After rounding 14.256 to 14.2 and 3.37 to 3.4, the estimated sum rounded to the nearest tenth is 17.6.
Step-by-step explanation:
To estimate the sum of 14.256 and 3.37 by first rounding each number to the nearest tenth, we should first identify the tenths place in each number. For 14.256, the tenths place is occupied by the digit 2, which means we round down to 14.2 because the hundredths place has a digit (5) that is less than 5. For 3.37, the tenths place has the digit 3, and we round up to 3.4 because the hundredths place is 7, which is greater than 5.
After rounding each number to the nearest tenth, we have 14.2 and 3.4. Adding these together, we get: 14.2 + 3.4 = 17.6. Thus, the estimated sum of 14.256 and 3.37, when rounded to the nearest tenth before adding, is 17.6.