Math Problem Statement
Rewrite as a simplified fraction.
[\large{3.\overline{2} = {?}}]
Solution
To express as a simplified fraction, we can follow these steps:
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Let , where the repeating part is .
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Multiply both sides of the equation by 10 to move the decimal point:
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Now subtract the original equation () from this new equation:
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Solve for by dividing both sides by 9:
Thus, as a simplified fraction is .
Would you like any more details on the steps? Here are 5 more questions for practice:
- Rewrite as a fraction.
- Express as a fraction.
- Convert to a fraction.
- How do you rewrite as a fraction?
- Simplify as a fraction.
Tip: When repeating decimals are converted to fractions, they often simplify to a ratio of two integers by manipulating algebraic expressions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Repeating Decimals
Fractions
Formulas
Let x = repeating decimal form
Multiply by powers of 10 to shift the decimal
Subtract equations to eliminate the repeating part
Solve for x and simplify
Theorems
Algebraic manipulation of repeating decimals
Conversion of repeating decimals to fractions
Suitable Grade Level
Grades 8-10