0.039 Repeating as a Fraction
Introduction
The decimal number 0.039 is a repeating decimal, which means that it has a pattern of digits that repeats indefinitely. In this article, we will explore how to convert 0.039 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, 0.12341234... is a repeating decimal because the sequence "1234" repeats indefinitely.
Converting 0.039 Repeating as a Fraction
To convert 0.039 repeating as 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 "039".
Step 2: Assign a Variable to the Repeating Pattern
Let's assign a variable x to the repeating pattern:
x = 0.039039039...
Step 3: Multiply the Variable by a Power of 10
Next, we multiply the variable x by a power of 10 to move the decimal point to the right:
100x = 3.903903903...
Step 4: Subtract the Original Variable from the Multiplied Variable
Now, we subtract the original variable x from the multiplied variable 100x:
100x - x = 3.903903903... - 0.039039039...
This simplifies to:
99x = 3.864
Step 5: Solve for x
Finally, we solve for x by dividing both sides of the equation by 99:
x = 3.864/99
x = 39/990
x = 13/330
Therefore, 0.039 repeating as a fraction is 13/330.
Conclusion
In this article, we have shown how to convert 0.039 repeating as a fraction. By following the steps outlined above, we can convert any repeating decimal to a fraction.
