2.26 Repeating as a Fraction
When dealing with decimal numbers, it's often necessary to convert them into fractions. In this case, we're going to explore how to convert the repeating decimal 2.26 into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 2.26, the sequence "26" repeats indefinitely, making it a repeating decimal.
Converting Repeating Decimals to Fractions
To convert a repeating decimal into a fraction, we can use the following steps:
- Let the repeating decimal be x: Let's say the repeating decimal is x.
- Multiply x by 100: Multiply x by 100 to get 226.26 (since the repeating part is 26).
- Subtract x from the result: Subtract x from 226.26 to get 226.26 - x = 224.
- Simplify the fraction: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD).
Converting 2.26 into a Fraction
Using the steps above, let's convert 2.26 into a fraction:
- Let x = 2.26
- Multiply x by 100: 2.26 × 100 = 226.26
- Subtract x from the result: 226.26 - 2.26 = 224
- Simplify the fraction: 224 ÷ 100 = 56/25
Therefore, 2.26 repeating as a fraction is equal to 56/25.
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