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anonymous

  • one year ago

What is the rational number equivalent to 3 point 24 with a bar over 24? 3 and 6 over 97 3 and 28 over 99 3 and 8 over 33 3 and 10 over 32

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  1. anonymous
    • one year ago
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    help

  2. jdoe0001
    • one year ago
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    hmmm test the given choices, see which one gives you \(\bf 3.\overline{24}\iff 3.242424242424...\)

  3. anonymous
    • one year ago
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    \[3.242424....=3+.24+.0024+.000024+...\] .24+.0024+.000024+... find the sum of infinite G.P

  4. mathstudent55
    • one year ago
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    |dw:1438125550660:dw|

  5. mathstudent55
    • one year ago
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    The whole part is 3. Let's try to find the fraction equivalent to 0.242424...

  6. mathstudent55
    • one year ago
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    Since 0.242424... has a repeating 2-digit pattern, we use the number 100 (which has 2 zeroes following the 1)

  7. mathstudent55
    • one year ago
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    Let x = 0.242424...

  8. mathstudent55
    • one year ago
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    |dw:1438125675580:dw|

  9. mathstudent55
    • one year ago
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    Now we use the number 100. We multiply both sides of x = 0.242424... by 100 and write above x = 0.242424... |dw:1438125735514:dw|

  10. mathstudent55
    • one year ago
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    Now we subtract the bottom equation from the top equation. |dw:1438125774875:dw|

  11. mathstudent55
    • one year ago
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    Now we solve for x and reduce: |dw:1438125803637:dw|

  12. mathstudent55
    • one year ago
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    Since we now know that 0.242424... = 8/33, we can finish the problem: 3.242424... = 3 8/33

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