Problem: Express 0.111... + 0.121212... + 0.123123123... as a repeating decimal and its equivalent fraction. Show work. Also, are there any extensions to this problem? In other words, are there any questions that we could ask that may be related to this problem?

Thank you!

The periods of the repeating parts of the three decimal fractions that you want to add are 1, 2 and 3 so the period of the repeating part of their sum may be as large as 6, the least common multiple of 1, 2 and 3. One way to approach this problem is to write the three decimal fractions to 12 places each and add to see the repeating pattern. You would need to then express the sum as a fraction. Another approach would be to express the three decimal fractions as fractions and then perform the addition.

An example of the process used to transform a repeating decimal to its equivalent fraction can be found in a previous question that we answered.

To see some other problems related to your question go to the Quandaries and Queries section of Math Central and search in the keyword field for the word repeating.