Converting 0.166 Repeating to a Fraction
Ever wondered how to convert a repeating decimal to a fraction? In this article, we'll explore the steps to convert 0.166 repeating to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a repeating pattern of digits. In the case of 0.166 repeating, the digits "166" repeat indefinitely. Repeating decimals can be converted to fractions, which can be useful in various mathematical applications.
Converting 0.166 Repeating to a Fraction
To convert 0.166 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.166...
Let's start by letting x equal 0.166 repeating.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal point.
1000x = 166.166...
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to eliminate the repeating decimal.
999x = 166
Step 4: Simplify the fraction
Divide both sides of the equation by 999 to simplify the fraction.
x = 166/999
Step 5: Simplify the fraction further
We can simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 166 and 999 is 83.
x = 2/9
Therefore, 0.166 repeating is equal to the fraction 2/9.
Conclusion
In this article, we've shown how to convert 0.166 repeating to a fraction using a simple step-by-step process. This process can be applied to any repeating decimal to convert it to a fraction. Remember to always simplify the fraction to its simplest form to make it easier to work with.
