## 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

1. anonymous

help

2. jdoe0001

hmmm test the given choices, see which one gives you $$\bf 3.\overline{24}\iff 3.242424242424...$$

3. anonymous

$3.242424....=3+.24+.0024+.000024+...$ .24+.0024+.000024+... find the sum of infinite G.P

4. mathstudent55

|dw:1438125550660:dw|

5. mathstudent55

The whole part is 3. Let's try to find the fraction equivalent to 0.242424...

6. mathstudent55

Since 0.242424... has a repeating 2-digit pattern, we use the number 100 (which has 2 zeroes following the 1)

7. mathstudent55

Let x = 0.242424...

8. mathstudent55

|dw:1438125675580:dw|

9. mathstudent55

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

Now we subtract the bottom equation from the top equation. |dw:1438125774875:dw|

11. mathstudent55

Now we solve for x and reduce: |dw:1438125803637:dw|

12. mathstudent55

Since we now know that 0.242424... = 8/33, we can finish the problem: 3.242424... = 3 8/33