Answer: [tex]\frac{104}{45}[/tex]
Step-by-step explanation:
[tex]2.31^-[/tex]
Let x be equal to that.
[tex]x=2.31^-[/tex]
Multiply by 1 followed by as many zeros as repeating numbers. In this case it's just one repeating decimal, therefore, 1 followed by 1 zero or 10.
[tex]10x=2.31^-*10[/tex]
This basically moves the decimal point one number to the right.
[tex]10x=23.11^-[/tex]
Subtract the first equation from this new equation.
[tex]10x=23.11^-\\-x=2.31^-[/tex]
--------------------------
The repeating decimal is eliminated and we are left with:
23.1
- 2.3
---------
20.8
We also have 10 - 1 = 9. We are left with:
[tex]9x=20.8[/tex]
Divide by 9.
[tex]x=\frac{20.8}{9}[/tex]
To get rid of the decimal, multiply by 1 followed by as many zeros as decimals. In this case 1.
[tex]x=\frac{20.8}{9} (\frac{10}{10} )[/tex]
[tex]x=\frac{208}{90}[/tex]
Let's simplify.
208/2=104
90/2=45
[tex]x=\frac{104}{45}[/tex]
