Math Problem Statement
Solution
The problem asks to convert the repeating decimal into a fraction.
Let's solve this step by step:
Step 1: Set up the repeating decimal
Let which means:
Step 2: Eliminate the repeating part
To eliminate the repeating decimal, multiply both sides of the equation by 100 (since the repeating part consists of two digits):
Step 3: Subtract the two equations
Now subtract the original equation from :
Step 4: Solve for
Now, divide both sides by 99:
Step 5: Simplify the fraction
The greatest common divisor (GCD) of 93 and 99 is 3. So divide both the numerator and the denominator by 3:
Thus, .
Would you like more details or have any questions?
Here are 5 related questions for practice:
- Convert into a fraction.
- Express as a fraction in simplest form.
- How would you convert to a fraction?
- What is the fractional equivalent of ?
- Simplify as a fraction.
Tip: For repeating decimals, the number of digits in the repeating sequence determines how many powers of 10 to multiply by.
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Math Problem Analysis
Mathematical Concepts
Repeating Decimals
Fraction Conversion
Simplifying Fractions
Formulas
x = 0.93̅
100x - x = 93.93̅ - 0.93̅
x = 93/99
Theorems
Greatest Common Divisor (GCD)
Decimal to Fraction Conversion
Suitable Grade Level
Grades 7-10