As illustrated below, and by other available solutions, this application will order a list of numbers from least to greatest and from greatest to least with the aid of a place value chart.
Students in the 6th grade should be able to order a list of numbers to include decimal numbers up to the thousandths place under Common Core standards. Like comparing decimal numbers, understanding the concept of place values is necessary to order a list of numbers.
The digits of each number should be vertically aligned by place or inserted into a place value chart. Thereafter, the digits should be compared by place from left to right. In other words, they should be compared from greatest place value to smallest place value if necessary. If the digits in the same place are equal, then a comparison between the digits in the place to the immediate right must be made. The number with the largest digit in the place being compared such as the Tenths place is the largest number. But unlike comparing two numbers, that procedure must be repeated for the remaining numbers in a list greater than two numbers.
For example, given the list: 3.455, 3.651, and 3.444. All three numbers have a 3 in the Ones place. However, they have different digits in the Tenths place. The 6 in the Tenths place in 3.651 is larger than the 4 in the Tenths place in 3.455. And it is also larger than the 4 in the Tenths place in 3.444. Therefore, 3.651 is the greatest number in the list. Now we have to compare the remaining two numbers (3.455 and 3.444). As noted above, we have to look to the place to the immediate right of the Tenths place (Hundredths place) since both numbers have a 4 in the Tenths place. Upon doing so, we can conclude that 3.455 is greater than 3.444 because the 5 in the Hundredths place in 3.455 is larger than the 4 in the Hundredths place in 3.444. From greatest to least: 3.651, 3.455, 3.444.
As illustrated by the example below, the application above returns a place value chart. Each digit of each number in the list of numbers entered are inserted into the chart. Notably, the numbers and digits are inserted in the chart from top to bottom according to the order selected. And where applicable, placeholder 0s are added to the right of the decimal point in the chart. In other words, the chart provides a clear visual as to why the numbers are correctly ordered in accordance with the selection from least to greatest (ascending order), or from greatest to least (descending order).