Math Problem Statement
Convert 0,13 to common fraction,when only 3 is recurring
Solution
To convert (where only the 3 is recurring) into a fraction, let’s follow these steps:
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Let .
So,
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Multiply both sides by 10 to shift the decimal point one place:
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Subtract the original equation from this new equation to eliminate the recurring decimal:
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This simplifies to:
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Now, solve for by dividing both sides by 9:
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Convert to a fraction:
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Simplify by dividing the numerator and the denominator by their greatest common divisor, 6:
So, .
Would you like more details or have any questions?
Here are some related questions:
- How can you convert other recurring decimals to fractions?
- What is the general formula for converting single-digit recurring decimals?
- How would the approach differ for a decimal where multiple digits recur?
- How do you simplify fractions effectively?
- Can recurring decimals always be represented as fractions?
Tip: When converting recurring decimals to fractions, multiply by powers of 10 that align the recurring digits for easy subtraction.
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Math Problem Analysis
Mathematical Concepts
Recurring Decimals
Fractions
Algebra
Formulas
x = 0.1\overline{3}
10x - x to eliminate recurring decimals
Simplifying fractions
Theorems
Conversion of recurring decimals to fractions
Suitable Grade Level
Grades 8-10