Math Problem Statement
Convert i.010101 to fraction
Solution
To convert the repeating decimal to a fraction, we can follow these steps:
-
Let . This means .
-
To eliminate the repeating part, multiply by 1000000 (since the repeating block is 6 digits long):
- Now, subtract the original from this equation:
- Solving for :
Therefore,
To simplify this fraction:
- The greatest common divisor (GCD) of 10101 and 999999 needs to be determined. Using the Euclidean algorithm or a calculator, we find:
- Divide both the numerator and the denominator by their GCD:
Thus, the simplified fraction form of is:
If you have any questions or need further details, feel free to ask!
Here are 5 related questions:
- How do you convert other repeating decimals to fractions?
- What is the Euclidean algorithm for finding the greatest common divisor (GCD)?
- How do you add fractions with different denominators?
- What are some methods for simplifying fractions?
- How do repeating decimals differ from terminating decimals in fraction form?
Tip: When converting repeating decimals to fractions, always determine the length of the repeating sequence and use it to form the appropriate equation.
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Math Problem Analysis
Mathematical Concepts
Repeating Decimals
Fractions
Simplification
Greatest Common Divisor (GCD)
Formulas
x = 0.010101... → 1000000x = 10101.010101...
1000000x - x = 10101 → 999999x = 10101 → x = 10101 / 999999
Simplify by dividing numerator and denominator by GCD(10101, 999999)
Theorems
Euclidean Algorithm
Suitable Grade Level
Grades 9-12