0.77 Repeating as a Fraction
What is 0.77 Repeating?
0.77 repeating, also known as 0.772727..., is a non-terminating and non-repeating decimal. This means that the digits 7 repeat indefinitely in a predictable pattern.
Converting 0.77 Repeating to a Fraction
To convert 0.77 repeating to a fraction, we can use a few different methods. One method is to use the following formula:
x = 0.772727...
Multiply both sides of the equation by 100 to get:
100x = 77.272727...
Now, subtract the original equation from the new equation:
100x - x = 77.272727... - 0.772727...
This simplifies to:
99x = 77
Divide both sides by 99:
x = 77/99
So, 0.77 repeating as a fraction is equal to 77/99.
Simplifying the Fraction
We can simplify the fraction 77/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 77 and 99 is 11. So, we can divide both numbers by 11:
77 ÷ 11 = 7 99 ÷ 11 = 9
This simplifies the fraction to 7/9.
Conclusion
In conclusion, 0.77 repeating as a fraction is equal to 77/99, which can be simplified to 7/9. This shows that a non-terminating and non-repeating decimal can be converted into a simple fraction.
