0.48282 Repeating as a Fraction
The decimal 0.48282 is a repeating decimal, where the sequence "4828" repeats indefinitely. To convert this decimal to a fraction, we can use a few mathematical techniques.
Method 1: Converting Repeating Decimals to Fractions
Let's assume the repeating decimal is represented by the variable x:
x = 0.48282...
To eliminate the repeating part, we can multiply both sides of the equation by 10,000 (since the repeating sequence has 4 digits):
10,000x = 4,828.2828...
Now, subtract the original equation from this new equation to eliminate the repeating part:
10,000x - x = 4,828.2828... - 0.48282...
This simplifies to:
9,999x = 4,827.8
Simplifying the Fraction
Divide both sides of the equation by 9,999 to get:
x = 4,827.8 / 9,999
Simplifying the fraction, we get:
x = 164/333
So, the repeating decimal 0.48282 is equal to the fraction 164/333.
Method 2: Long Division
Another way to convert the repeating decimal to a fraction is to use long division. This method involves dividing the numerator (the repeating decimal) by the denominator (1).
Here's the long division process:
_______________________
1 | 0.48282...
- 0.48
_______________________
0.0082
- 0.008
_______________________
0.0002
- 0.0002
_______________________
0.0000
The quotient is the fraction 164/333, which is the same result as the previous method.
Conclusion
In conclusion, the repeating decimal 0.48282 is equal to the fraction 164/333. This can be achieved using either method: eliminating the repeating part or using long division.
