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Math Notebook & Pencil Converting Rational Numbers to Fractions

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Steps Step 1: Let x equal the repeating decimal you are trying to convert to a fraction Step 2: Examine the repeating decimal to find the repeating digit(s) Step 3: Place the repeating digit(s) to the left of the decimal point

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Steps Cont. Step 4: Place the repeating digit(s) to the right of the decimal point Step 5: Subtract the left sides of the two equations.Then, subtract the right sides of the two equations As you subtract, just make sure that the difference is positive for both sides

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Example What rational number or fraction is equal to 0.55555555555? Step 1: x = 0.5555555555 Step 2: After examination, the repeating digit is 5 Step 3: To place the repeating digit ( 5 ) to the left of the decimal point, you need to move the decimal point 1 place to the right 0.55555555 5.55555

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Technically, moving a decimal point one place to the right is done by multiplying the decimal number by 10. When you multiply one side by a number, you have to multiply the other side by the same number to keep the equation balanced Thus, 10x = 5.555555555

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Step 4 Place the repeating digit(s) to the right of the decimal point Look at the equation in step 1 again. In this example, the repeating digit is already to the right, so there is nothing else to do. x = 0.5555555555

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Step 5 Your two equations are: 10x = 5.555555555 x = 0.5555555555 10x - x = 5.555555555 0.555555555555 9x = 5 Divide both sides by 9 x = 5/9

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Example #2 What rational number or fraction is equal to 1.04242424242 Step 1: x = 1.04242424242 Step 2: After examination, the repeating digit is 42

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Why 3 places? Step 3: To place the repeating digit ( 42 ) to the left of the decimal point, you need to move the decimal point 3 place to the right

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Why Miss Greger? Again, moving a decimal point three place to the right is done by multiplying the decimal number by 1000. When you multiply one side by a number, you have to multiply the other side by the same number to keep the equation balanced Thus, 1000x = 1042.42424242

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Step 4 Place the repeating digit(s) to the right of the decimal point In this example, the repeating digit is not immediately to the right of the decimal point. Look at the equation in step 1 one more time and you will see that there is a zero between the repeating digit and the decimal point To accomplish this, you have to move the decimal point 1 place to the right

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Step 5 Your two equations are: 1000x = 1042.42424242 10x = 10.42424242 1000x - 10x = 1042.42424242 10.42424242 990x = 1032 Divide both sides by 990 x = 1032/990

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Try by yourself 0.4444444 0.787878787 0.997997997