Final answer:
The repeating decimal 0.9 bar is equal to the fraction 1/1 or simply 1. This can be shown using algebra to set up equations and isolate the decimal.
Step-by-step explanation:
The repeating decimal 0.9 bar can be expressed as a fraction in the simplest form. To do this, we need to set up an equation using algebraic variables to represent known and unknown values.
Step 1: Let's express 0.9 bar as a variable, x in the form of: x = 0.9...
Step 2: Multiply both sides of the equation by a power of 10 to shift the decimal point to the right, specifically 10x = 9.9...
Step 3: Subtract the original equation from the new equation to get rid of the decimal. The result is: 10x - x = 9, which simplifies to 9x = 9. Then, we divide both sides by 9 to isolate x, giving us the fraction x = 1.
So, 0.9 bar as a fraction is 1/1 or simply 1.
Learn more about Repeating Decimal to Fraction