Comparing and ordering

Arrange seventy two thousand, six hundred and fifteen, seventy two thousand, one hundred and sixty five and seventy one thousand, six hundred and twenty five in ascending order. Try it first. Pause if you like. Ascending order means smallest first. Which place should we compare first? Start at the largest place. All three numbers have 7 in the ten thousands place. Those digits agree, so move to the thousands. Which value is smaller? The third number has 1 thousand. Its thousands digit has a value of one thousand. The first two numbers each have 2 thousands. That value is two thousand. One thousand is less than two thousand. So seventy one thousand, six hundred and twenty five is the smallest. Now compare the two numbers still tied. Their ten thousands and thousands digits are the same. In these two numbers, compare the hundreds next. The second number has 1 hundred, with a value of one hundred. The first number has 6 hundreds, with a value of six hundred. One hundred is less than six hundred. This settles the tied pair before we reach the tens or ones. So, from smallest to greatest, the order is seventy one thousand, six hundred and twenty five, seventy two thousand, one hundred and sixty five, and seventy two thousand, six hundred and fifteen. The first place that differs decides. The question tells us which end comes first.

Arrange forty thousand, nine hundred and twenty eight, forty thousand, two hundred and eighty nine, forty thousand, nine hundred and eighty two and forty thousand, two hundred and ninety eight in descending order. Try it first. Pause if you like. Descending order means greatest first. Begin at the largest place again. The ten thousands and thousands digits are the same in all four numbers. Compare the hundreds. This separates the four numbers into two pairs. The first and third numbers each have 9 hundreds. The value is nine hundred. The second and fourth numbers each have 2 hundreds. The value is two hundred. Nine hundred is greater than two hundred. The two numbers with 9 hundreds come first. For the pair with 9 hundreds, compare the tens. Eighty is greater than twenty, so the third number is greater. For the pair with 2 hundreds, compare the tens. Ninety is greater than eighty, so the fourth number is greater. So, from greatest to smallest, the order is forty thousand, nine hundred and eighty two, forty thousand, nine hundred and twenty eight, forty thousand, two hundred and ninety eight, and forty thousand, two hundred and eighty nine. The first place that differs decides. The question tells us which end comes first.