How do you convert -0.13 (3 being repeated) to a fraction?

Question

HIX Tutor · Accepted Answer

undefined To convert -0.133333... to a fraction, follow these steps:

1. **Let x = -0.13333...**  
   (This means the 3 repeats.)

2. **Multiply both sides by 10:**  
   $ 10x = -1.3333... $

3. **Now, subtract the first equation from the second:**  
   $ 10x - x = -1.3333... - (-0.1333...) $

4. **This simplifies to:**  
   $ 9x = -1.2 $

5. **Now, divide both sides by 9:**  
   $ x = -\frac{1.2}{9} $

6. **Convert -1.2 to a fraction:**  
   $ -\frac{1.2}{9} = -\frac{12}{90} $

7. **Simplify the fraction:**  
   $ -\frac{12}{90} = -\frac{2}{15} $

So, -0.13333... as a fraction is **-2/15**.

Eva Abramson · Answer

#-2/15#

We first let -0.13 (3 being repeated) be #x#.

Since #x# is recurring in 1 decimal places, we multiply it by #10^1#.

#10x = -1.33#

We then deduct them.

#10x - x = -1.33 - (-0.13)#

#9x = -1.2#

Lastly, we divide both sides by 9 to get #x# as a fraction.

#x = -1.2/9#

#= -12/90#

#= -2/15#

Genesis Allen · Answer

#-0.13#
#x=-0.133#
#10x=-1.33#
#100x=-13.33#
#100x-10x=-13.33-1.33#
#90x=-14.66#
#x=-1466/9000#
now cancel it by yourself

Genesis Allen · Answer

undefined To convert the decimal -0.13 (with 3 repeating) to a fraction, you can use the concept of infinite geometric series. Since the decimal repeats, we can represent it as -0.13̅. To convert it to a fraction, set x = -0.13̅ and subtract it from 100 times x. This gives you 100x - x = 13̅. Then, solve for x to get x = -13̅/99. So, -0.13̅ is equivalent to -13̅/99 as a fraction.

Eva Adamson · Answer

undefined To convert the recurring decimal -0.13333... to a fraction, use the following method:

Let x = -0.13333...

Multiply both sides by 100 to eliminate the repeating decimal:
100x = -13.33333...

Subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x - x = -13.33333... - (-0.13333...)
99x = -13.2

Divide both sides by 99 to solve for x:
x = -13.2 / 99

Therefore, the fraction equivalent of -0.13 (repeating) is -$\frac{132}{990}$.