08333 As A Fraction

Amer Zain

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08-12-2024

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Converting the decimal 0.8333 (assuming it's a repeating decimal, indicated by the trailing 3s) into a fraction requires a few simple steps. Here's how to do it:

Understanding Repeating Decimals

The key to converting repeating decimals to fractions is recognizing the repeating pattern. In 0.8333..., the digit 3 repeats infinitely. We need to account for this repetition to get an accurate fractional representation.

Step-by-Step Conversion

1. Let x equal the decimal: We begin by assigning a variable, typically 'x', to represent our repeating decimal:

   x = 0.8333...

2. Multiply to shift the repeating part: We multiply both sides of the equation by a power of 10 that shifts the repeating part to the left of the decimal point. Since the repeating digit is 3, we multiply by 10:

   10x = 8.3333...

3. Subtract the original equation: Subtracting the original equation (x = 0.8333...) from the modified equation (10x = 8.3333...) eliminates the repeating portion:

   10x - x = 8.3333... - 0.8333... 9x = 7.5

4. Solve for x: We now solve for x to find the equivalent fraction:

   x = 7.5 / 9

5. Simplify the fraction: To express the fraction in its simplest form, we can multiply both the numerator and denominator by 2 to remove the decimal:

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

   Then we simplify the fraction by finding the greatest common divisor (GCD) of 15 and 18, which is 3. Dividing both the numerator and denominator by 3, we get:

   x = 15/18 = 5/6

Therefore, 0.8333... as a fraction is 5/6.

Important Note on Non-Repeating Decimals

If the decimal number were not repeating (e.g., 0.8333), the conversion process would be different. We would simply write it as a fraction with the decimal part over a power of 10 (e.g., 8333/10000). This fraction could then be simplified if necessary. Always examine the decimal carefully to determine if it repeats before applying the appropriate conversion method.