0.54 Repeating as a Fraction
What is 0.54 Repeating?
0.54 repeating is a decimal number that has a repeating pattern of digits. In this case, the digits "54" repeat indefinitely to form the decimal 0.545454.... This type of decimal is also known as a repeating decimal or a recurring decimal.
Converting 0.54 Repeating to a Fraction
To convert 0.54 repeating to a fraction, we can use the following steps:
Step 1: Let the repeating decimal be x
Let x = 0.545454...
Step 2: Multiply x by 100
Multiply x by 100 to get rid of the decimal point:
100x = 54.545454...
Step 3: Subtract x from 100x
Subtract x from 100x to eliminate the repeating pattern:
100x - x = 54.545454... - 0.545454... 99x = 54
Step 4: Divide by 99
Divide both sides by 99 to solve for x:
x = 54/99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD):
x = 54/99 = 27/49
Therefore, 0.54 repeating as a fraction is 27/49.
Conclusion
In conclusion, we have successfully converted 0.54 repeating to a fraction, which is 27/49. This process can be used to convert any repeating decimal to a fraction.
