.71 Repeating as a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions in simplest form. One such repeating decimal is .71, which equals 71/99. But how do we arrive at this fraction? Let's dive into the process.
Understanding Repeating Decimals
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of .71, the sequence "71" repeats indefinitely, making it a repeating decimal.
Converting .71 to a Fraction
To convert .71 to a fraction, we can use the following steps:
Step 1: Let x = .71
Let's assume x equals .71.
Step 2: Multiply x by 100
Multiplying x by 100 gives us:
100x = 71.71
Step 3: Subtract x from 100x
Subtracting x from 100x gives us:
99x = 71
Step 4: Divide by 99
Dividing both sides of the equation by 99 gives us:
x = 71/99
Thus, .71 equals 71/99 in simplest form.
Simplifying the Fraction
In this case, the fraction 71/99 is already in simplest form. However, if the fraction had common factors, we would need to simplify it further.
Conclusion
In conclusion, .71 repeating equals 71/99 in simplest form. By following the steps outlined above, we can convert any repeating decimal into a fraction in simplest form. This is an important concept in mathematics, as it allows us to simplify complex decimals and perform calculations with ease.
