5.3+Exploring+Repeating+Decimals

11/18/08 KSL

Notes: none taken


 * A.** Copy the table below, and write each fraction as a decimal.


 * Fraction || 1/9 || 2/9 || 3/9 || 4/9 || 5/9 || 6/9 || 7/9 || 8/9 ||
 * Decimal || 0.11111... || 0.22222... || 0.33333... || 0.44444... || 0.55555... || 0.66666... || 0.77777... || 0.88888... ||


 * B.** Describe the pattern you see in your table.

As the fraction increases by 1 the decimal increases by one.


 * C.** Use the pattern to write a decimal representation for each fraction. Use your own calculator to check your answers.

1. 9/9=1 2. 10/9=1.111... 15/9= 1.666...


 * D.** What fraction is equivalent to each decial? (Hint: the number 1.222... can be written as 1 + 0.222...)


 * Follow-Up 5.3**


 * 1.** Explore the decimal representations of fractions with a denominator of 99. Try 1/99, 2/99, 3/99 and so on. What patterns do you see?

1/99= 0.010101...

2/99= 0.020202...

3/99= 0.030303...

pattern is the same as problem B but this time you add 0 between because the denominator is bigger.


 * 2.** Explore the decimal representations of fractions with a denominator of 999. Try 1/999, 2/999, 3/999, and so on. what patterns do you see?

1/999= 0.001001001...

2/999= 0.002002002...

3/999= 0.003003003...

patter is the same as problem number 2 on top but this time you add 0 again because the denominator is bigger.


 * 3.** Use the patterns you discovered in the decima representations of fractions with denominators of 9. 99, and 999 to find fractions with these decimal representations.

a. 0.3333...= 3/9 b. 0.05050505= 5/99 c. 0.454545= 45/99 d. 0.045045045...= 45/999 e. 10.121212...= 10 12/99 f. 3.999...=