0.17 Recurring as a Fraction in Simplest Form
What is 0.17 recurring?
0.17 recurring, also known as 0.17~, is a decimal number that has an infinite number of repeating digits. It can be written as 0.171717... where the digits 17 repeat indefinitely.
Converting 0.17 Recurring to a Fraction
To convert 0.17 recurring to a fraction, we can use the following steps:
Let x = 0.171717...
Multiply both sides by 100 to get:
100x = 17.171717...
Subtract x from both sides to get:
99x = 17
Divide both sides by 99 to get:
x = 17/99
So, 0.17 recurring as a fraction in simplest form is 17/99.
Simplification
To ensure that the fraction is in its simplest form, we can check if the numerator (17) and denominator (99) have any common factors. In this case, they do not, so the fraction 17/99 is already in its simplest form.
Conclusion
In conclusion, 0.17 recurring as a fraction in simplest form is 17/99. This conversion is useful in various mathematical calculations and applications where fractions are required.
