0.5333 Repeating as a Fraction
The decimal number 0.5333 with a repeating pattern of 3's can be converted to a fraction. In this article, we will show you how to do it.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In this case, the repeating pattern is 3, which means that the number can be written as 0.5333..., where the dots indicate that the sequence of 3's goes on forever.
Converting 0.5333 to a Fraction
To convert 0.5333 to a fraction, we can use the following steps:
Step 1: Identify the Repeating Pattern
The repeating pattern in 0.5333 is 3, which means that we can write the number as:
0.5333 = 0.5 + 0.0333...
Step 2: Let x = 0.0333...
Let x = 0.0333..., where x is a variable that represents the repeating pattern.
Step 3: Multiply both sides by 100
Multiply both sides of the equation by 100 to get:
100x = 3.33...
Step 4: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 3
Step 5: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 3/99
Step 6: Simplify the Fraction
Simplify the fraction 3/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
x = 1/33
Step 7: Write 0.5333 as a Fraction
Now that we have found x, we can write 0.5333 as a fraction:
0.5333 = 0.5 + x = 0.5 + 1/33 = 16/33
Conclusion
In conclusion, the decimal number 0.5333 with a repeating pattern of 3's can be converted to a fraction, which is 16/33. This process involves identifying the repeating pattern, setting up an equation, and simplifying the fraction to its lowest terms.
