.083 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we will explore how to convert .083 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, .083 is a repeating decimal because the sequence of digits 083 repeats infinitely.
Converting .083 Repeating to a Fraction
To convert .083 repeating to a fraction, we can use the following steps:
Step 1: Identify the Repeating Pattern
The first step is to identify the repeating pattern in the decimal number. In this case, the repeating pattern is 083.
Step 2: Multiply by a Power of 10
The next step is to multiply the decimal number by a power of 10 to move the decimal point to the right of the repeating pattern. Since the repeating pattern has three digits, we will multiply by 10^3 or 1000.
.083 × 1000 = 83.000
Step 3: Subtract the Original Value
Now, subtract the original value from the new value to eliminate the non-repeating part of the decimal.
83.000 - .083 = 82.917
Step 4: Simplify the Fraction
The resulting value is a fraction:
82917/999000
Simplifying 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 82917 and 999000 is 333.
(82917 ÷ 333) / (999000 ÷ 333) = 249 / 3000
So, the final answer is:
.083 repeating = 249/3000
Conclusion
In conclusion, we have successfully converted .083 repeating to a fraction, which is equal to 249/3000. This process can be applied to any repeating decimal to convert it into a fraction.
