Final answer:
To round 735.597 to the nearest tenth, we increase the tenths place from '5' to '6' as the hundredths place is '9', which is greater than 5, resulting in 735.6.
Step-by-step explanation:
When rounding a number to the nearest tenth, it is important to look at the digit in the hundredths place. For the number 735.597, the hundredths place is represented by the digit '9'. According to the rules of rounding, if the digit in the hundredths place is 5 or higher, you round up the tenths place by one unit. In this case, since the digit is '9', which is greater than 5, the tenths place digit '5' is increased by one, thus rounding 735.597 to 735.6 when rounded to the nearest tenth.
In practical applications, especially in fields like science and engineering, such precision and understanding of significant figures are very important. For instance, when adding quantities like in the provided examples, the final answer should reflect the least precise measurement. This means you round your answer to the same place value as the least precise measurement you're working with.