Is 0.541r a Simple Fraction or Radian Measure?

[Gringo123]

What is 0.541^r as a fraction? I have a feeling the answer won't be as simple as 541/1000.

 

[Cyosis]

Write it as a sum of 0.541+0.000541+0.000000541+... and use the geometric series.

 

[Gringo123]

Thanks Cyosis. I see that the answer would be 541/999.

 

[Cyosis]

Yes, that is correct.

 

[I like number]

What is 0.541^r as a fraction? I have a feeling the answer won't be as simple as 541/1000.

Hi,
I was taught what I consider a really neat trick for writing recurring decimals as fractions(supernerdy) and thought I'd share it. :D

let x = 0.54154141...
1000x=541.541541...
1000x-x=541
999x=541
x=541/999
0.541...=541/999
:D

It's probably easier to use Cyosis' method though :D

 

[danielatha4]

.aaaaaaaaaaaa ... = a/9
.abababababab ... = ab/99 (ab is not multiplication, simply the digits)
.abcabcabcabcabc ... = abc/999 (again, not multiplication between a b and c)

and so on

 

[Glenn L]

0.541r could also be interpreted as radian measure. In which case it might be an approximation of 0.54105 20681 18242 1 = 31 π / 180, or an angle of 31 degrees.

 

[Dickfore]

$$\begin{array}{rclr} x & = & 0.(541) & \. /\cdot 1000 \ (\mathrm{because \, the \, period \, is \, 3 \, decimal \, places \, long}) \\ 1000 x & = & 541.(541) & \end{array}$$

Subtract the two equations. What happens to the decimal part? Then solve for x and you should get your answer in a form of a fraction.

 

[HallsofIvy]

0.541r could also be interpreted as radian measure. In which case it might be an approximation of 0.54105 20681 18242 1 = 31 π / 180, or an angle of 31 degrees.

Yes, it could but given the title of this thread, that is extremely unlikely.