.93 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal like .93 into a fraction? In this article, we will explore the process of converting .93 repeating into a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of .93, the digits "93" repeat forever, making it a repeating decimal.
Converting .93 Repeating into a Fraction
To convert .93 repeating into a fraction, we can use the following steps:
Step 1: Let x = .93
Let's start by letting x equal .93.
Step 2: Multiply x by 100
Next, we multiply both sides of the equation by 100, which gives us:
100x = 93.93
Step 3: Subtract x from both sides
Now, we subtract x from both sides of the equation to get:
99x = 93
Step 4: Divide both sides by 99
Finally, we divide both sides of the equation by 99, which gives us:
x = 93/99
Simplifying the Fraction
We can simplify the fraction 93/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3. This gives us:
x = 31/33
The Final Answer
Therefore, .93 repeating as a fraction is equal to 31/33.
Conclusion
Converting repeating decimals into fractions can be a bit tricky, but by following these steps, you can easily convert any repeating decimal into a fraction. Remember to multiply by a power of 10 to move the decimal point, subtract the original value, and then simplify the fraction to get the final answer.
