What is 1/400 as a percent?

Converting fractions to a percentage can be very helpful. Let's go through the steps to change a decimal into a percentage.

You can try different values to learn more about the conversion process.

Often, convert 1/450 to a percent or 0.003 to a percent, depending on the task.

Determining the scaling factor:

Applying a scaling factor to convert fractions to percentages:

Solution:

For fractions:

In this guide, we’ll be focusing on the fraction 1/400 and how to convert it into its percentage equivalent.

Method 1 – Fraction Scaling:

1. Understanding Fractions: At the heart of every fraction, there's a division taking place. The numerator denotes the 'portions' we're focused on. The denominator reveals the total possible 'portions'. So, when we say $\frac{1}{400}$, we're essentially talking about 1 'portions' out of an available 400.
2. Explanation of Percentage: The term “Percent” has Latin roots, where “cent” means a hundred. So, a percentage essentially portrays a fraction where the denominator is always 100. For illustration, when we state 50%, it translates to 50 out of 100 or $\frac{50}{100}$ in fraction terms.
3. Transformation Process: To convert $\frac{1}{400}$ into a percentage, we must multiply the fraction to have 100 as its denominator. Begin by determining the factor by which 400 can be multiplied to get 100. This factor is $\frac{100}{400}\mathrm{=\; 0.25}$. Following this logic, multiply both the numerator and denominator by 0.25:$\frac{\mathrm{1\; \times \; 0.25}}{\mathrm{400\; \times \; 0.25}}\mathrm{=}\frac{0.25}{100}$.
4. Final Step: Once multiplied, the fraction denotes 0.25 out of 100, which is equivalent 0.25%.

Method 2 – Using Decimals:

1. Fraction to Decimal Transformation: Begin by expressing $\frac{1}{400}$ as a decimal. This step requires simple division: divide the numerator (1) by the denominator (400), resulting in 0.0025.
2. Decimal to Percentage Conversion: Now, transform this decimal into a percentage. So, 0.0025 multiplied by 100 equals 0.25%.
3. Wrapping Up: Through the decimal conversion method as well, $\frac{1}{400}$ is equivalent of 0.25% when expressed as a percentage.

Both methods, while distinct in approach, provide the same result. You can choose to use either the direct fraction scaling method or the decimal conversion method.

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