What is the fraction of 0.85 percent

General
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what is the fraction of 0.85 percent

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What is the fraction of 0.85 percent?

Answer:

To convert a percentage to a fraction, you need to follow a series of steps that simplify the percentage into a fraction form. Let’s focus on converting 0.85 percent into a fraction:

Step 1: Understanding Percentages

The term “percent” means “per hundred.” Therefore, when we say 0.85 percent, we are referring to 0.85 per 100. This representation would initially translate to the fraction \frac{0.85}{100}.

Step 2: Converting Decimal to Fraction

In its current form, the numerator of our fraction is a decimal (0.85), and we need to convert it into a whole number. To do this, consider the following simplification process:

  • Multiply both the numerator (0.85) and the denominator (100) by 100 to eliminate the decimal. This gives:

    \frac{0.85 \times 100}{100 \times 100} = \frac{85}{10000}

Step 3: Simplifying the Fraction

Now, we have the fraction \frac{85}{10000}. To simplify, we must find the greatest common divisor (GCD) for both 85 and 10000.

  1. Prime Factorization for 85: The factors are 1, 5, 17, and 85.

  2. Prime Factorization for 10000: The factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 5000, and 10000. The GCD in this case is 5.

  3. Dividing by the GCD: Divide both the numerator and the denominator by their GCD, which is 5:

\frac{85 \div 5}{10000 \div 5} = \frac{17}{2000}

This simplifies 85 divided by 5 equals 17, and 10000 divided by 5 equals 2000.

Final Answer:

Thus, the fraction form of 0.85 percent is:

\frac{17}{2000}

This fraction cannot be simplified further, making it the most reduced form of 0.85 percent.