CramX Logo

Q
QuestionMathematics

Convert 0.83 repeating to a fraction.
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

Step 1:
I'll solve this step by step using precise LaTeX formatting:

Step 2:
: Define the repeating decimal

Let $$x = 0.8\overline{3}$$ (where the bar indicates the repeating part)

Step 3:
: Multiply both sides by 10 to shift the decimal

10x = 8.3\overline{3}

Step 4:
: Subtract the original equation from the new equation

9x = 7.5
x = 0.8\overline{3}

Step 5:
: Solve for x

x = \frac{7.5}{9}

Step 6:
: Simplify the fraction

x = \frac{75}{90}
x = \frac{5}{6}

Final Answer

Verification: \frac{5}{6} = 0.8333... \checkmark