This document contains instructions for two parts of a math worksheet. Part 1 asks students to complete a table converting fractions to decimals and look for patterns in which fractions terminate or repeat. Part 2 asks students to fill out a table of seventh fractions and use long division to derive a conjecture about repeating decimal expansions.

1. Name______________________________
Digit Fidgits
Part 1: converting fractions to decimals
Complete the following table for the decimal expansions of the fractions listed. If you notice that
the decimal expansion is repeating, just write it once with a bar over it.
1/1 1/11 1/21
1/2 1/12 1/22
1/3 1/13 1/23
1/4 1/14 1/24
1/5 1/15 1/25
1/6 1/16 1/26
1/7 1/17 1/27
1/8 1/18 1/28
1/9 1/19 1/29
1/10 1/20 1/30
Are there any patterns that you notice? Which fractions terminate after only a few decimal
values? Why is this so? Can you create a relationship between the denominator and the number
of decimal places?

2. Part 2: cycle lengths
To derive a conjecture about repeating decimal expansions, fill out the table below of sevenths
expansions.
1. What pattern do you notice?
2. Why do you think it occurs?
3. Now, expand 1/7 by using long division.
4. Look at your long division process from number 3. What remainders occurred during
your process? Put the numbers 0-6 in a circle. Draw lines with arrows to show how one
remainder leads to another.
1/7
2/7
3/7
4/7
5/7
6/7