Video Transcript
The table shows the populations of five countries in a given year. List the countries from the smallest to the largest population.
In this question, we need to order the population sizes of five countries from smallest to largest using a table. We can start by noting that the population sizes are given in scientific notation. That is the form 𝑎 times 10 raised to the power of 𝑛, where the absolute value of 𝑎 lies between one and 10 and 𝑛 is an integer.
This gives us two ways of answering this question. We could convert all of the populations into normal form. However, we can directly compare the sizes of numbers given in standard form by comparing the sizes of 𝑎 and 𝑛. We can start by noting that the exponent of 10 in the population of country C is the smallest. Since the populations must be positive, this means that country C must have the smallest population. One way of seeing this is to note that its population number will have the least number of digits.
In the same way, we can see that country B will have a larger population than country C, since its population size has an extra digit. But it will have a smaller population than the rest of the countries since its exponent of 10 is smaller. This process works to order the other three countries. We get the order C, B, D, E, A.
However, there are a few things worth noting about this method. First, we used the fact that the populations are positive. If they were not positive, then we would also need to consider the signs of the numbers to help us order them. Second, we may not always have different exponents of 10 for each of the numbers. For instance, imagine we added an extra country F onto the table with a population of 5.35 times 10 raised to the power of eight. We know that country F has a larger population than countries C, B, D, and E, since the exponent of 10 is larger. However, we would still need to compare its population size to that of country A. Since the exponents of 10 are the same, we can do this by comparing the size of the first factor. We know that 5.3 is smaller than 5.35. So country A has a smaller population than country F. So, in this case we would add country F to have the largest population.
However, in our question, we were able to show that the order of the countries from smallest population to largest population is C, B, D, E, A.
