The discussion revolves around expressing the repeating decimal 10.1(35) as a ratio of two integers. Participants are exploring methods related to geometric series and algebraic manipulation to achieve this representation.
Participants are actively sharing different approaches and questioning each other's methods. Some guidance has been offered regarding the alignment of repeating parts in the equations, but there is no explicit consensus on the correct method yet.
There appears to be confusion regarding the correct manipulation of the decimal and the setup of equations, with some participants noting discrepancies in their calculations and assumptions about the repeating decimal.
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