0.0707 Repeating as a Fraction
Have you ever wondered what the fraction equivalent of the repeating decimal 0.0707 is? In this article, we'll explore how to convert this repeating decimal to a fraction.
Understanding Repeating Decimals
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.0707, the sequence "07" repeats indefinitely. To convert a repeating decimal to a fraction, we need to find the equivalent ratio of integers.
Converting 0.0707 to a Fraction
To convert 0.0707 to a fraction, we can use the following steps:
Step 1: Let x = 0.0707
Let x be equal to 0.0707.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 7.0707
Step 3: Subtract x from both sides
Subtract x from both sides to eliminate the x term.
99x = 7
Step 4: Divide by 99
Divide both sides by 99 to solve for x.
x = 7/99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
x = 1/14
Therefore, the fraction equivalent of the repeating decimal 0.0707 is 1/14.
Conclusion
In this article, we've successfully converted the repeating decimal 0.0707 to a fraction. By following these simple steps, you can convert any repeating decimal to a fraction. Remember to always simplify your fraction by dividing both the numerator and denominator by their GCD.
