What is 0.8333333333 in fraction form?
The Correct Answer and Explanation is :
The decimal 0.8333333333 (repeating) can be written as the fraction 5/6. Here’s a detailed explanation of how to convert the repeating decimal to a fraction:
Step-by-Step Conversion
- Identify the repeating decimal:
The decimal 0.8333333333… repeats the digit 3 indefinitely after the decimal point. We can write this as 0.\overline{3}, where the overline indicates that the 3 repeats infinitely. - Let the repeating decimal be represented by a variable:
Let x = 0.\overline{3}. This means that x is equal to the repeating decimal. - Multiply both sides by 10:
To shift the decimal point one place to the right, multiply both sides of the equation by 10:
[
10x = 8.3333333333…
] - Subtract the original equation from the new equation:
Now, subtract the equation x = 0.8333333333… from 10x = 8.3333333333… to eliminate the repeating decimals:
[
10x – x = 8.3333333333… – 0.8333333333…
]
This simplifies to:
[
9x = 7.5
] - Solve for x:
To find x, divide both sides of the equation by 9:
[
x = \frac{7.5}{9}
] - Simplify the fraction:
The fraction 7.5/9 can be simplified by multiplying both the numerator and denominator by 10 to remove the decimal point:
[
x = \frac{75}{90}
]
Now, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 15:
[
x = \frac{75 \div 15}{90 \div 15} = \frac{5}{6}
]
Conclusion:
Therefore, 0.\overline{3} = 5/6. This means that the repeating decimal 0.8333333333… is equivalent to the fraction 5/6.