Round any whole number to a required degree of accuracy 2 - Reasoning

In a reasoning task focused on number and place value, students are presented with a real-world problem involving the comparison of population sizes of two cities – Mexico City and New York – which have been rounded to different degrees of accuracy. Esin believes that New York has a larger population than Mexico City because the figures provided are 11 million and 11.2 million respectively. However, this conclusion is challenged by the concept that rounding to different points can lead to inaccurate comparisons. Mexico City's population is rounded to the nearest million, which means it could range from 10,500,000 to 11,499,999, while New York's is rounded to the nearest hundred thousand, indicating a population range from 11,150,000 to 11,249,999. To accurately compare the populations, both figures must be rounded to the same point.

The dialogue between Esin and Zach illustrates a common misconception when comparing numbers that have been rounded to different degrees. The answer to the task clarifies that Esin's assumption is incorrect, as the overlap in possible population ranges due to the different rounding points means that one cannot definitively state which city has the larger population without further information. This exercise highlights the importance of understanding the implications of rounding and the need for a consistent degree of accuracy when making comparisons between rounded numbers.