Activity 6.1: Decimal Patterns

Purpose: Explore patterns with fractions and decimals.
When do fractions repeat as decimals? When do fractions terminate as decimals?

Materials: Base-ten blocks, paper, calculator, spreadsheet

Part 1: Models

Make 5 different proper decimals with base-ten blocks. Sketch the base-ten blocks and write down the number they represent in decimal and fraction form. You may use the Number Pieces app Links to an external site.. Be sure to Identify what one whole is.

Part 2: Calculators

1. Use your calculator to convert the following fractions to decimals. Use = if the decimal terminates and ≈ if it does not.
   1.   1/2
   2.   1/3
   3.   1/4
   4.   1/5
   5.   1/6
   6.   1/7
   7.   1/8
   8.   1/9
   9.   1/10
2. Based on these examples make a hypothesis as to when a fraction will terminate as a decimal and when a fraction will repeat as a decimal.

Part 3: Spreadsheet

1. Build a spreadsheet with rows for denominators up to 32 and columns for some numerators.

For example:

Each decimal should be calculated by the spreadsheet.

2. Based on these examples revise your hypothesis as to when a fraction will terminate as a decimal and when a fraction will repeat as a decimal.