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BITS AND PIECES III INVESTIGATION 3.4 REPRESENTING FRACTIONS AS DECIMALS What are terminating decimals? Terminating decimals are numbers that do not repeat when divided. When you take 1 and divide it by 2, you get 0.5. When you take 1 and divide it by 4, you get 0.25. What are repeating decimals? What are repeating decimals? Repeating decimals are numbers that repeat. When doing 1 divided by 3 the number never ends and continuously repeats 3 after 0. When doing 1 divided by 11 the number never ends and continuously repeats 09 after 0. Why do fractions like 1/2 and 1/4 also have terminating decimal forms? Why do fractions like 1/2 and 1/4 also have terminating decimal forms? Because they can make equivalent fractions with denominators of 10, 100, 1000, etc. 1/2 = 5/10; 1/4 = 25/100 1.) 2/5 = 4/10 = 0.4 2.) 3/8 = 375/1000 = 0.375 3.) 5/6 is Repeating = 0.83333...... 4.) 35/10 = 3.5 5.)8/99 is Repeating = 0.8888...... 1.) 2/5 = 4/10 = 0.4 2.) 3/8 = 375/1000 = 0.375 3.) 5/6 is Repeating = 0.83333...... 4.) 35/10 = 3.5 5.)8/99 is Repeating = 0.8888...... 1/4, 2/8, 4/16, 5/20, 6/24, 25/100 = 0.25 The decimal matches the fraction that has 10, 100, 1000, etc. as a denominator 25/100 = 0.25 35/100 21456/10000 89050/100000= 8905/10000 214560/100000= 21456/10000 1/3, 1/6, 1/9, 5/15 1. To tell whether a fraction has a terminating or repeating decimal representation, examine it in its simplest form. Fractions with terminating decimals only have 2’s and/or 5’s in the prime factorization of the denominator. Fractions with repeating decimals will have factors other than 2 or 5 in the denominator. 2. There is no repeating decimal with 10, 100, 1000, etc. as its denominator.