08333 as a fraction

Breiz Heurope

2 min read

·

10-03-2025

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The decimal 0.8333... (where the 3s repeat infinitely) represents a repeating decimal. Converting repeating decimals to fractions is a straightforward process. Let's break down how to convert 0.8333... into its fractional equivalent.

Understanding Repeating Decimals

A repeating decimal is a decimal number where one or more digits repeat infinitely. In our case, the digit 3 repeats endlessly. We often denote this with a bar over the repeating digits: 0.8$\bar{3}$.

Converting 0.8333... to a Fraction

Here's the method to convert 0.8333... to a fraction:

1. Set up an equation:

Let x = 0.8333...

2. Multiply to shift the decimal:

Multiply both sides of the equation by 10 to shift the repeating part to the left of the decimal point:

10x = 8.3333...

3. Subtract the original equation:

Now, subtract the original equation (x = 0.8333...) from the new equation (10x = 8.3333...):

10x - x = 8.3333... - 0.8333...

This simplifies to:

9x = 7.5

4. Solve for x:

Divide both sides by 9 to isolate x:

x = 7.5 / 9

5. Simplify the fraction:

To simplify, multiply both the numerator and denominator by 2 to get rid of the decimal in the numerator:

x = (7.5 * 2) / (9 * 2) = 15/18

Now, we simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:

x = 15/18 = 5/6

Therefore, 0.8333... is equal to 5/6.

Verification

We can verify our answer by performing long division: 5 ÷ 6 = 0.8333... This confirms our conversion is correct.

Alternative Method (for simpler repeating decimals)

For repeating decimals where only the digits after the decimal point repeat, a quicker method exists. However, this method doesn't directly apply to 0.8333... because the 8 is not part of the repeating sequence.

Let's consider a simpler example: 0.333...

1. The repeating digit is 3.
2. The fraction is 3/9.
3. Simplify: 3/9 = 1/3

This illustrates the pattern, but the method with the multiplication and subtraction is more universally applicable and is the preferred method for decimals such as 0.8333...

Conclusion

Converting repeating decimals like 0.8333... to fractions involves a systematic approach. By following the steps outlined above, you can accurately transform any repeating decimal into its equivalent fraction. Remember to always simplify the fraction to its lowest terms for the most concise representation. The fraction 5/6 is the simplest and most accurate representation of the repeating decimal 0.8333...