American football uses a field that is 100.0 yd long, whereas a soccer field is 100.0 m long. Which field is longer, and by how much (give yards, meters, and percent)?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. In order to compare a soccer field and a football field, we have to compare the same units and so we'll convert the 100 yards of a football field into meters by multiplying by 3 feet for every yard and the yards cancel and then multiply that by 1 meter for every 3.281 feet and then that gives us 91.44 meters is the length of a football field in meters. So soccer field is 100 meters minus 91.4355 meters which is 8.6 meters longer than a football field and we can express that length difference in yards by taking the unrounded difference there— 8.5645 meters—times by 3.281 feet for every meter, the meters cancel and times by 1 yard for every 3 feet, the feet cancel leaving us with 9.4 yards. Oh by the way, this has precision to the tenths place because when you are doing addition or subtraction, your answer will be precise to the digit the most precise digit in the least precise number you are working with. So this 100.0 is the least precise number that we are working with; it's precise only to the tenths place whereas the length for the football field is precise— well, I put it all the way over to here— ten thousandths place. But so the tenths place is the best precision that we can have in our answer and so that's why we round this to 8.6. And since we are working with a number that's precise only to the tenths place, that's why our answer here is also precise only to the tenths place. And then we look at percent difference and we have a 100 meters minus 91.4355 meters divided by 91.4355 meters and this tells us that the soccer field is 9.4 percent longer than a football field. And this is precise to the tenths place because this difference up here is, I don't now, 8. something or other and that can be precise only to the tenths place and so 8. something is gonna have two significant figures so when we do this division by 91.4355, our answer to that division can have only two significant figures and so that's why we have 9.4 here.