## Thursday, 5 February 2015

### Investigating Recurring Decimals

Our Investigation... with a spreadsheet, we generated the decimals for fractions from 1/1 to 1/50:

Below is part of what we have generated...

During the lesson, we learnt that there are some limitations from the spreadsheet (software), which includes the number of decimals that it could display. As a result, the we are unable to conclude if some fractions could be converted to recurring decimals or not.

e.g. 1/23 a recurring decimal?
From the spreadsheet, we are unable to observe any repeating pattern of numbers.

Using another online application, Wolfram Alpha, we get:
In fact, 1/23 is a recurring decimal with a period of "22"

Similarly, with Wolfram Alpha, we get:
1/29 results a recurring decimal with a period of "28"

From the above, we can conclude that all rational number can be expressed as either a recurring decimal or a terminating decimal.

Hence, other real numbers that are non-recurring and non-terminating are irrational numbers.

Extension...

Now, look at the fractions and the resulting recurring decimals.
Look out for some interesting patterns of the recurring decimals... are you able to draw out some patterns?
Hint: Look out for the characteristics of some of the denominators

Enter your observations below... remember to key in your group number before submission.