Since palindromic decimals are more fun when they are shared, students can work together in groups to experiment with them. Learning how to make palindromic numbers is a good activity with which to start. The process is very simple; you add a number to its reverse and keep going until you have a palindrome. One example is: 3.2 + 2.3 = 6.6 + 6.6 = 13.2 + 2.31 = 15.51. This took three steps. Students can next be asked to find out if all two-digit decimals take only three steps to make a palindrome. They can find out by figuring out how many steps it takes to make a palindromic decimal from these two-digit decimals: 1.7, 6.4, 2.9, 8.5, and 7.3. The answers are: 1.7 becomes 37.73 in four steps, 6.4 becomes 11.11 in two steps, 2.9 becomes 13.31 in two steps, 8.5 becomes 17.71 in two steps, and 7.3 becomes 11.11 in two steps.
Students can do another activity to find out if any two-decimal number can be made into a palindrome. Working in groups, students should apply the same process to these two digit numbers: .43, 5.0, .06, .25, .81 The answers are: .43 becomes 34.43 in one step, 5.0 becomes 5.5 in one step, .06 becomes 60.06 in one step, .285 becomes 582.285 in one step, .81 becomes 18.81 in one step.
Next, students can work with three digit decimals. First, ask the students to apply the same process of adding the reverse to these numbers: 1.72, .593, 22.7, .081, 4.09. The answers are 1.72 becomes 28.82, .593 becomes 395.593, 22.7 becomes 29.92, .081 becomes 180.081, and 4.09 becomes 94.49. After students have done this process, they can answer several questions and test their hypotheses. They can be asked how many steps did each one take? The answer is one step. They can next be asked: Do you think this will be true of all three-digit decimals? Students should test five more numbers to justify their answers. There are only four that will not form a palindrome with less than 23 steps. If you add up the digits of these four they will equal 25, so if your computations take more than a few steps, try adding the digits to see if it is an exception to the rule. Students can also be offered extra credit if they can figure out the four numbers that have a decimal and three digits that take more than 23 steps to make a palindrome. They can use calculators. There are only 18 possible combinations of numbers with a decimal that add up to 25.
To take the activity to the next step, students can test a few four-digit numbers. Ask students to apply the same process to these: 43.64, 123.4, .9015, 98.23. The answers are: 43.64 becomes 89.98 in one step, 123.4 becomes 127.721 in one step, .9015 becomes 5109.9015 in one step, and 98.23 becomes 152.251 in two steps.