The discussion focuses on expressing the repeating decimal 10.1(35) as a ratio of two integers. The correct approach involves defining S as 10.135353535... and setting up two equations: 1000S = 10135.353535... and 10S = 101.353535... Subtracting these equations yields 990S = 10034, leading to the final result of S = 5017/495. This method effectively aligns the repeating parts of the decimal for accurate calculation.
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jbreezy said:Homework Statement
express the number as a ratio of integers.
10.1(35) = 10.135353535 the part in the left in () is where is is over lined to indicate it is repeating
Homework Equations
geometric series
The Attempt at a Solution
10.1(35) = 10.1 + .035 = (101)/ (1000) + (35/10^3 + 35/10^6...)
= 101/1000 + ((35/1000)/(1-(1000)) = .1360350
clearly wrong. What did i mess up
No you don't. 10135.353535... - 10.135353535... ≠ 10125Jbreezy said:Yeah that is actually what I did but I did it different. I said that it was Because I thought that you had to move the decimal to the end of the first repeating number.So in my case I said 10.1(35) the I have to move it to after the 5 so I multiply by 1000. My two equations will read.
S = 10.135353535
1000x = 10135.353535
Do the subtraction and you get 999x = 10125 So I ended up with 375/37
So that the repeating part lines up in both numbers.Jbreezy said:Why did you have 10S I just had x