0.037 Recurring as a Fraction
Introduction
Recurring decimals, also known as repeating decimals, are a type of decimal number that has a sequence of digits that repeats indefinitely. In this article, we will explore how to convert the recurring decimal 0.037 into a fraction.
What is a Recurring Decimal?
A recurring decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a recurring decimal because the sequence "1234" repeats indefinitely. Recurring decimals can be converted into fractions, which is a more compact and useful way to represent them.
Converting 0.037 Recurring into a Fraction
To convert 0.037 recurring into a fraction, we can use the following steps:
Step 1: Let's assume that the recurring decimal is x.
x = 0.037037...
Step 2: Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 3.703703...
Step 3: Subtract x from both sides of the equation to eliminate the recurring part.
100x - x = 3.703703... - 0.037037...
Step 4: Simplify the equation.
99x = 3.666666...
Step 5: Divide both sides of the equation by 99 to solve for x.
x = 3.666666... / 99
x = 1/27
Therefore, the recurring decimal 0.037 recurring is equal to the fraction 1/27.
Conclusion
In this article, we have learned how to convert the recurring decimal 0.037 into a fraction. By following the steps outlined above, we can convert any recurring decimal into a fraction. This is a useful skill to have in mathematics, as fractions are often easier to work with than decimals.
