0.1 6 Repeating as a Simplified Fraction
In mathematics, repeating decimals can be converted into simplified fractions. One such example is 0.1 6 repeating, which can be written as a fraction in its simplest form.
What is 0.1 6 Repeating?
0.1 6 repeating is a decimal number that has a repeating pattern of 16. It can be written as:
0.1616... or 0.16̇
The dot above the 6 indicates that the sequence repeats indefinitely.
Converting 0.1 6 Repeating to a Simplified Fraction
To convert 0.1 6 repeating to a simplified fraction, we can use the following steps:
Let x = 0.1616...
Multiply both sides by 100 to get rid of the decimal places:
100x = 16.16...
Subtract x from both sides to eliminate the repeating pattern:
99x = 16
Divide both sides by 99 to solve for x:
x = 16/99
So, 0.1 6 repeating can be written as a simplified fraction:
16/99
Conclusion
In conclusion, the repeating decimal 0.1 6 can be converted into a simplified fraction, which is 16/99. This shows that even seemingly complex decimal numbers can be expressed in a more compact and elegant form using fractions.
