.416 as a Repeating Decimal: A Fractional Representation
In mathematics, decimal numbers can be expressed in different forms, including fractions. One such decimal number is .416, which has a fascinating property of being a repeating decimal. In this article, we'll explore .416 as a repeating decimal and its equivalent fractional representation.
What is a Repeating Decimal?
A repeating decimal, also known as a recurring decimal, is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a repeating decimal, where the sequence "1234" repeats endlessly.
.416 as a Repeating Decimal
The decimal number .416 is a repeating decimal, and its sequence of digits repeats every four digits. The repeating pattern can be written as:
.416416416...
This pattern continues indefinitely, making .416 a repeating decimal.
Converting .416 to a Fraction
To convert .416 to a fraction, we can use a few different methods. One approach is to use the formula:
a = d/99
where a is the repeating decimal and d is the repeating sequence of digits. In this case, a = .416 and d = 416.
Using this formula, we can calculate the fraction as:
.416 = 416/999
This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 416 and 999 is 83, so we can simplify the fraction as:
.416 = 416/999 = 52/249
Therefore, the fractional representation of .416 is 52/249.
Conclusion
In this article, we've explored .416 as a repeating decimal and its equivalent fractional representation. By converting .416 to a fraction, we've discovered that it can be expressed as 52/249. This conversion demonstrates the versatility of decimal numbers and their relationships with fractions.
