.97 Repeating as a Fraction
When we see a repeating decimal like .97, it's often easier to understand and work with it as a fraction. But how do we convert .97 to a fraction? In this article, we'll explore the process and find the answer.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of .97, the sequence "97" repeats forever. Repeating decimals can be converted to fractions, and vice versa.
Converting .97 to a Fraction
To convert .97 to a fraction, we can use the following steps:
- Let x = .9797...
- Multiply both sides by 100 to get 100x = 97.9797...
- Subtract x from both sides to get 99x = 97
- Divide both sides by 99 to get x = 97/99
So, .97 repeating is equal to the fraction 97/99.
Simplifying the Fraction
We can simplify the fraction 97/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 97 and 99 is 1, so the fraction is already in its simplest form.
Conclusion
In conclusion, .97 repeating is equal to the fraction 97/99. By using the steps outlined above, we can convert any repeating decimal to a fraction. This is useful in many mathematical applications, such as algebra, geometry, and calculus. Remember, converting between decimals and fractions is an important skill in mathematics!
