0.14 Repeating as a Fraction in Simplest Form
What is 0.14 Repeating?
0.14 repeating is a decimal number that has a never-ending sequence of digits. It can be written as 0.141414... where the digits 14 repeat indefinitely.
Converting 0.14 Repeating to a Fraction
To convert 0.14 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.1414...
Let's assume that x = 0.1414... .
Step 2: Multiply both sides by 100
To get rid of the decimal point, we multiply both sides of the equation by 100.
100x = 14.1414...
Step 3: Subtract the original equation from the new equation
Subtract x = 0.1414... from 100x = 14.1414... to eliminate the repeating decimal.
99x = 14
Step 4: Simplify the fraction
Divide both sides of the equation by 99 to get:
x = 14/99
Simplifying the Fraction
The fraction 14/99 is already in its simplest form.
Final Answer
Therefore, 0.14 repeating as a fraction in simplest form is 14/99.
Note: This method can be used to convert any repeating decimal to a fraction in simplest form.
