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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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

Mathematics
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hmmm test the given choices, see which one gives you \(\bf 3.\overline{24}\iff 3.242424242424...\)
\[3.242424....=3+.24+.0024+.000024+...\] .24+.0024+.000024+... find the sum of infinite G.P

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Other answers:

|dw:1438125550660:dw|
The whole part is 3. Let's try to find the fraction equivalent to 0.242424...
Since 0.242424... has a repeating 2-digit pattern, we use the number 100 (which has 2 zeroes following the 1)
Let x = 0.242424...
|dw:1438125675580:dw|
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|
Now we subtract the bottom equation from the top equation. |dw:1438125774875:dw|
Now we solve for x and reduce: |dw:1438125803637:dw|
Since we now know that 0.242424... = 8/33, we can finish the problem: 3.242424... = 3 8/33

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