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Converting Rational Numbers to Fractions

Converting Rational Numbers to Fractions. Math Notebook & Pencil . 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 )

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Converting Rational Numbers to Fractions

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  1. Converting Rational Numbers to Fractions Math Notebook & Pencil

  2. 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

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

  4. 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

  5. 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 balancedThus, 10x = 5.555555555

  6. Step 4 • Place the repeating digit(s) to the right of the decimal pointLook 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

  7. Step 5 • Your two equations are:10x = 5.555555555   x = 0.555555555510x - x = 5.555555555 − 0.5555555555559x = 5Divide both sides by 9x = 5/9

  8. 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

  9. 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

  10. 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 balancedThus, 1000x = 1042.42424242

  11. Step 4 • Place the repeating digit(s) to the right of the decimal pointIn 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 pointTo accomplish this, you have to move the decimal point 1 place to the right

  12. Step 5 • Your two equations are:1000x = 1042.42424242   10x = 10.424242421000x - 10x = 1042.42424242 − 10.42424242990x = 1032Divide both sides by 990x = 1032/990

  13. Try by yourself • 0.4444444 • 0.787878787 • 0.997997997

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