0.16 Repeating as a Simplified Fraction
What is 0.16 Repeating?
0.16 repeating is a decimal number that has a sequence of digits that repeats indefinitely. In this case, the sequence of digits "16" repeats over and over again. This type of decimal is also known as a repeating decimal or a non-terminating decimal.
Converting 0.16 Repeating to a Fraction
To convert 0.16 repeating to a simplified fraction, we can use a few different methods. One method is to set up an equation using the repeating decimal as a fraction.
Let's say the repeating decimal 0.16 is equal to a fraction, x:
$x = 0.1616...$
We can multiply both sides of the equation by 100 to get:
$100x = 16.16...$
Now, we can subtract the first equation from the second equation to get:
$99x = 16$
Dividing both sides of the equation by 99, we get:
$x = \frac{16}{99}$
Simplified Fraction
So, the simplified fraction equivalent to 0.16 repeating is:
$\frac{16}{99}$
This fraction is in its simplest form, meaning that the numerator and denominator have no common factors.
Conclusion
In this article, we have seen how to convert the repeating decimal 0.16 to a simplified fraction. By using a simple equation and some algebraic manipulation, we were able to find the equivalent fraction, which is 16/99.
