Converting 0.370 Repeating to a Fraction
Have you ever wondered how to convert a repeating decimal to a fraction? In this article, we'll explore how to convert 0.370 repeating to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.370 repeating, the sequence "370" repeats indefinitely.
Converting 0.370 Repeating to a Fraction
To convert 0.370 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.370 Repeating
Let's start by letting x = 0.370 repeating.
Step 2: Multiply Both Sides by 1000
Next, we'll multiply both sides of the equation by 1000 to get rid of the decimal point.
1000x = 370.370 repeating
Step 3: Subtract x from Both Sides
Now, let's subtract x from both sides of the equation to get rid of the repeating decimal.
1000x - x = 370.370 - 0.370 990x = 370
Step 4: Divide Both Sides by 990
Finally, we'll divide both sides of the equation by 990 to solve for x.
x = 370/990 x = 37/99
The Final Answer
Therefore, 0.370 repeating as a fraction is 37/99.
Conclusion
In this article, we've successfully converted 0.370 repeating to a fraction using a simple step-by-step process. By multiplying both sides of the equation by 1000, subtracting x, and dividing by 990, we were able to convert the repeating decimal to the fraction 37/99.
