Convert 3.33 Repeating Decimal To A Fraction

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Converting repeating decimals to fractions is a common task in mathematics. In this article, we'll show you how to convert the repeating decimal 3.33... into a fraction. This skill is useful for algebra, calculus, and other areas of math.

Understanding Repeating Decimals

A repeating decimal is a decimal number that has a digit or a group of digits that repeat infinitely. The repeating part is indicated by a bar over the repeating digits or by writing the digits followed by '...'.

Why Convert Repeating Decimals to Fractions?

Converting repeating decimals to fractions makes it easier to perform exact arithmetic operations. Fractions represent precise values, whereas decimals are often rounded for practical purposes. — Nelson County Bust: Details Released

Converting 3.33... to a Fraction: Step-by-Step

Here’s how to convert the repeating decimal 3.33... to a fraction:

  1. Set up an equation:

    Let x = 3.33...

  2. Multiply by 10:

    Multiply both sides of the equation by 10 to shift the decimal point one place to the right: 10x = 33.33...

  3. Subtract the original equation:

    Subtract the original equation (x = 3.33...) from the new equation (10x = 33.33...): 10x - x = 33.33... - 3.33... 9x = 30

  4. Solve for x:

    Divide both sides by 9 to solve for x: x = 30 / 9

  5. Simplify the fraction:

    Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3: x = (30 ÷ 3) / (9 ÷ 3) x = 10 / 3

So, the repeating decimal 3.33... is equal to the fraction 10/3.

Alternative Method

Another approach involves recognizing that 3.33... is 3 + 0.33.... Since 0.33... is 1/3, then 3.33... = 3 + 1/3 = 9/3 + 1/3 = 10/3. — NC Public Offender Search: How To Find Criminal Records

Examples of Other Repeating Decimals

  • 0.666... = 2/3
  • 0.111... = 1/9
  • 0.142857142857... = 1/7

Conclusion

Converting repeating decimals to fractions is a straightforward process involving algebraic manipulation. By following these steps, you can accurately convert any repeating decimal into its fractional equivalent, which is essential for various mathematical applications.

Understanding how to convert repeating decimals to fractions is a fundamental skill in mathematics. By using the methods described above, you can confidently convert 3.33... and other repeating decimals into fractions. — Gibi ASMR OnlyFans: What Makes It So Popular?