The following question has two parts. First, answer part A. Then, answer part B.
Jadyn and Leah were in a fishing tournament. Jadyn's fish weighed 2.120 kilograms. Leah's fish weighed 2.12 kilograms.
Part A
Jadyn says his fish weighs more because 120 is larger than 12. Is he correct? Explain your answer. Use place value to support your thinking.
(4 points)
No, Jadyn is not correct. When comparing the numbers 120 and 12, we have to consider their place values. In 120, the 1 is in the hundreds place, the 2 is in the tens place, and the 0 is in the ones place. In 12, the 1 is in the tens place and the 2 is in the ones place. Although 120 has a larger digit 1 in the hundreds place compared to the tens place in 12, the tens place has a larger value than the hundreds place. The tens place has a value of 10, whereas the hundreds place has a value of 100. Therefore, 12 is actually greater than 120. In the case of Jadyn's fish and Leah's fish, although Jadyn's fish weighs 2.120 kilograms and Leah's fish weighs 2.12 kilograms, the difference in the weight is much smaller than the difference in the numbers 120 and 12. Therefore, we cannot conclude that Jadyn's fish weighs more based on the comparison of 120 and 12 alone.
Part A:
No, Jadyn is not correct. Although 120 is a larger number than 12, we need to consider the place value in this context. Place value refers to the value of each digit in a number based on its position. In the given weights, Jadyn's fish weighs 2.120 kilograms, while Leah's fish weighs 2.12 kilograms.
In Jadyn's fish weight, the digit 1 is in the "hundredths" place, the digit 2 is in the "tenths" place, and the digit 0 is in the "ones" place. Therefore, we read it as 2.120 kilograms.
In Leah's fish weight, the digit 1 is in the "tenth" place, and the digit 2 is in the "ones" place. Therefore, we read it as 2.12 kilograms.
Comparing the weights using place value, we see that 2.12 kilograms is actually larger than 2.120 kilograms. This is because in Jadyn's fish weight, the "hundredths" place has a 0, which means it contributes no additional weight. Therefore, Leah's fish, with a weight of 2.12 kilograms, is actually heavier than Jadyn's fish with a weight of 2.120 kilograms.