Converting 0.84 (Repeating) to a Fraction
What is 0.84 (Repeating)?
0.84 (repeating) is a decimal number that has a repetitive pattern of digits. In this case, the pattern is "84" repeating indefinitely, i.e., 0.848484... The repeating part is often denoted by a horizontal line or a vinculum above the digits, like this: 0.84̄.
Converting to a Fraction
To convert 0.84 (repeating) to a fraction, we can use a simple trick. Let's assume that the repeating decimal is equal to a variable, say x:
x = 0.848484...
Step 1: Multiply by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 84.8484...
Step 2: Subtract the Original Equation
Subtract the original equation from the new equation:
100x - x = 84.8484... - 0.8484...
This simplifies to:
99x = 84
Step 3: Divide by 99
Divide both sides of the equation by 99:
x = 84/99
Simplifying the Fraction
The fraction 84/99 can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 3:
x = 28/33
And that's it! We have successfully converted 0.84 (repeating) to a fraction:
0.84 (Repeating) = 28/33
This fraction represents the exact value of the repeating decimal.
