Materials:

Computers with spreadsheet program Repeating & Terminating spreadsheet: repeating.xls (13.5 KB)

Environment:
One computer classroom, classroom lab

Strategy:
Students can work

1. Begin by asking the students what the difference is between a number expressed as a fraction and a number expressed as a decimal. If necessary, you may need to review equivalent fractions as described in the Learn More section of this activity.
   • Two fractions are clones if they are equivalent. For example, 3/4 = 75/100 is read “seventy five hundredths” and equals .75
     (BTW - If you say .75 with meaning, you say “75 hundredths”, not “point 75”)
2. Then, you should follow-up with the following lead-in question:
   • Can every fraction be written as a decimal?
   • For example, 1/3 can’t be cloned to have 10, 100, 1000, etc. in its denominator because you can’t come up with a whole number to clone with for 3 since 3 does not divide into 10, 100, 1000, etc. evenly. Therefore, the best we can do is to treat 1/3 as a division problem (which it is) and do the division: 1/3 = 0.3333333...... (here 3 is the repeating number).

Procedure (Doing the Activity)

1. Print and distribute the Activity page.
2. Open the repeating.xls spreadsheet on a projector or overhead and describe the four columns, where Column A identifies the fraction, Column B displays the equivalent decimal, Column C identifies if the number has a terminating or repeating decimal, and Column D identifies the number(s) greater than 0 that are repeated.
   • For example, 1/3 = .333333..... has a Repeating decimal and there is one number (3) that is repeated and greater than 0.
3. Ask the students either individually or in groups to complete instructions, beginning with the repeating.xls spreadsheet.
4. Once students have completed the repeating.xls spreadsheet, they should respond to the question "Can you tell ahead of time whether a fraction will repeat or terminate?" individually and explain their answers. Time permitting, it is recommended to have a class discussion about this question after students have been provided with sufficient time to complete their answers.

Assessment (Debrief)
Understanding the difference between Terminating and Repeating Decimals can be challenging for students who have a fragile or limited understanding of fractions. One strategy could be to use manipulatives wherever possible.

After students have completed the repeating.xls spreadsheet, ask the students to print-out copies and hand in their results with the answer to the question on their handout to serve as an assessment.

Extensions & Additional Activities

• Exploring Repeating and Terminating Decimals
• Developing the Concept: Terminating and Repeating Decimals
• Recurring decimal