# Homework Help: 0.541 recurring as a fraction

1. May 11, 2010

### Gringo123

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

2. May 11, 2010

### Cyosis

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

3. May 11, 2010

### Gringo123

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

4. May 11, 2010

### Cyosis

Yes, that is correct.

5. May 15, 2010

### I like number

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

6. May 15, 2010

### 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

7. Jun 26, 2010

### 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.

8. Jun 26, 2010

### 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.

9. Jun 26, 2010

### HallsofIvy

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