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Convert the following in p/q form. (1) 23.456 [ 56 is repeating ] (2) 5.3278 [ 78 is repeating ] ?
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Convert the following in p/q form. (1) 23.456 [ 56 is repeating ] (2) ...
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Convert the following in p/q form. (1) 23.456 [ 56 is repeating ] (2) ...
Conversion of Decimal to Fraction


Example 1

Convert 23.456 [56 is repeating] to p/q form


Solution:


  • Let x = 23.45656565656...

  • Multiply both sides by 100 to get rid of the decimal:


    • 100x = 2345.6565656565...


  • Subtract x from 100x:


    • 100x - x = 2345.6565656565... - 23.45656565656...

    • 99x = 2322


  • Divide both sides by 99:


    • x = 2322/99


  • Therefore, 23.456 [56 is repeating] = 2322/99



Example 2

Convert 5.3278 [78 is repeating] to p/q form


Solution:


  • Let x = 5.3278787878...

  • Multiply both sides by 100 to get rid of the decimal:


    • 100x = 532.78787878...


  • Subtract x from 100x:


    • 100x - x = 532.78787878... - 5.3278787878...

    • 99x = 527.46


  • Divide both sides by 99:


    • x = 527.46/99


  • Therefore, 5.3278 [78 is repeating] = 527.46/99

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Convert the following in p/q form. (1) 23.456 [ 56 is repeating ] (2) 5.3278 [ 78 is repeating ] ?
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