.24 Repeating as a Fraction
The decimal .24 repeating, also written as .242424..., is a recurring decimal that can be converted into a fraction. In this article, we will explore how to convert .24 repeating into a fraction and discuss some of its properties.
Converting .24 Repeating into a Fraction
To convert .24 repeating into a fraction, we can use the following steps:
Step 1: Let x = .242424...
Let x be equal to .242424....
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 24.242424...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 24
Step 4: Divide by 99
Divide both sides of the equation by 99 to get:
x = 24/99
Simplifying the Fraction
We can simplify the fraction 24/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 24/99 = 8/33
Therefore, .24 repeating is equal to 8/33 as a fraction.
Properties of .24 Repeating
Now that we have converted .24 repeating into a fraction, let's explore some of its properties:
Rational Number
.24 repeating is a rational number because it can be expressed as a fraction, namely 8/33.
Repeating Decimal
.24 repeating is a repeating decimal because it has a sequence of digits that repeats indefinitely.
** Equivalent Fractions**
8/33 is an equivalent fraction of .24 repeating, which means that they have the same value.
Conclusion
In this article, we have seen how to convert .24 repeating into a fraction, specifically 8/33. We have also explored some of the properties of .24 repeating, including its rationality, repeating decimal nature, and equivalent fractions.
