0.27 Repeating as a Fraction
What is 0.27 Repeating?
0.27 repeating is a decimal number that has a recurring pattern of digits. In this case, the decimal part of the number is 0.27, and it repeats indefinitely. This type of number is also known as a repeating decimal or a recurring decimal.
Converting 0.27 Repeating to a Fraction
To convert 0.27 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.272727...
Let x be equal to 0.27 repeating.
Step 2: Multiply x by 100
Multiply x by 100 to get:
100x = 27.272727...
Step 3: Subtract x from 100x
Subtract x from 100x to get:
99x = 27
Step 4: Solve for x
Divide both sides of the equation by 99 to get:
x = 27/99
Simplifying the Fraction
We can simplify the fraction 27/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 9.
x = 27/99 = 3/11
Therefore, 0.27 repeating as a fraction is equal to 3/11.
Conclusion
In conclusion, 0.27 repeating can be converted to a fraction, which is equal to 3/11. This process involves multiplying the decimal by a power of 10, subtracting the original decimal, and solving for the variable.
