What is 0.083 repeting as a percentage?
The Correct Answer and Explanation is:
To convert the repeating decimal (0.083\overline{3}) (where the “3” repeats indefinitely) into a percentage, we can follow a systematic approach.
Step 1: Define the Decimal
Let (x = 0.083333…). Here, the “3” after the “8” is the repeating part.
Step 2: Eliminate the Repeating Decimal
To eliminate the repeating part, we multiply (x) by (10) (to shift the decimal point one place to the right) to get:
[
10x = 0.83333…
]
Now we subtract the original (x) from this equation:
[
10x – x = 0.83333… – 0.08333…
]
This simplifies to:
[
9x = 0.75
]
Step 3: Solve for (x)
Now, divide both sides by (9):
[
x = \frac{0.75}{9} = \frac{75}{900} = \frac{1}{12}
]
Step 4: Convert to Percentage
To convert (x) to a percentage, we multiply by (100):
[
x \times 100 = \frac{1}{12} \times 100 = \frac{100}{12} \approx 8.3333…
]
Thus, (0.0833\overline{3}) as a percentage is approximately (8.33\%).
Step 5: Conclusion
The repeating decimal (0.0833\overline{3}) can be accurately expressed as (8.33\%). This conversion is significant in various fields such as finance and statistics, where precise calculations are essential. For instance, understanding percentages is crucial when interpreting data, making financial decisions, or calculating interest rates.
In summary, converting repeating decimals to percentages involves identifying the repeating sequence, creating an equation to isolate the decimal, and then multiplying by (100) to obtain the percentage. This method is both systematic and effective, ensuring accurate results in mathematical and real-world applications.