0.16 Repeating as a Simplified Fraction Calculator
When dealing with repetitive decimals, it's often helpful to convert them into simplified fractions to make calculations easier and more intuitive. In this article, we'll explore how to convert 0.16 repeating into a simplified fraction using a calculator.
What is 0.16 Repeating?
0.16 repeating, also written as 0.1616..., is a decimal that continues indefinitely in a repetitive pattern. This type of decimal is known as a recurring decimal or a reptend.
Converting 0.16 Repeating to a Simplified Fraction
To convert 0.16 repeating into a simplified fraction, we can follow these steps:
Step 1: Let x = 0.1616...
Let's assume x = 0.1616... for simplicity.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 16.16...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 16
Step 4: Divide by 99
Divide both sides of the equation by 99 to get:
x = 16/99
Simplified Fraction
The simplified fraction equivalent to 0.16 repeating is:
16/99
Using a calculator, we can verify that 16/99 is indeed equal to 0.1616...
Conclusion
Converting 0.16 repeating into a simplified fraction using a calculator is a straightforward process. By following the steps outlined above, we can easily convert repetitive decimals into fraction form, making calculations and comparisons easier and more intuitive.
Calculator Tip
If you have a calculator with a fraction conversion feature, you can simply enter 0.16 repeating and convert it to a fraction. The calculator will automatically simplify the fraction for you, giving you the result: 16/99.
