Order and Compare Numbers up to 10 Million 4 - Reasoning

In a reasoning task about ordering and comparing numbers up to 10 million, students Mal and Tia are presented with two numbers and asked to determine which one is larger. Mal suggests comparing the hundreds place, noting that the first number has a 0 while the second has a 1, implying that the first number is smaller. Tia, on the other hand, looks at the ten-thousands place, observing that the first number has a 1, which is larger than the 0 in the second number. The numbers in question are 7,442,075 and 7,442,174. The correct approach to determine which number is larger involves a place value comparison starting from the highest value place. In this case, since the numbers are identical up to the thousands place, the comparison should begin from the hundreds place.

Upon examining the hundreds place, it is clear that the first number has a 0 and the second number has a 1, indicating that the second number is larger because it has a greater value in the hundreds place. Therefore, Mal's reasoning is correct, and Tia's focus on the ten-thousands place is misplaced since the numbers only differ in the hundreds place. Consequently, the statement that 7,442,075 is larger than 7,442,174 is incorrect. Similarly, the comparison of 5,010,268 and 5,009,368 also requires careful consideration of place value. The correct comparison would show that 5,010,268 is indeed larger than 5,009,368, as the first number has a greater value in the ten-thousands place, despite the second number having a higher value in the hundreds place. Thus, understanding place value is essential for accurately ordering and comparing large numbers.