Question

Write the fraction as a decimal and as a percent. $$ \frac{4}{25} $$

Short answer

The fraction \( \frac{4}{25} \) as a decimal is 0.16, and as a percent is 16%.

Step-by-step solution

Convert the fraction to a decimal

To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). By dividing 4 by 25, we get 0.16.

Convert the decimal to a percent

To convert a decimal to a percent, multiply by 100. So, 0.16 would become \(0.16 * 100 = 16\%\) when represented as a percentage.

Key concepts

Fraction to Decimal Conversion

Understanding how to transform a fraction into a decimal is an essential math skill. The process is straightforward: divide the numerator (top number of the fraction) by the denominator (bottom number of the fraction). For instance, consider the fraction \( \frac{4}{25} \).

To convert this fraction to a decimal, we simply perform the division of 4 by 25. Executing this division results in the decimal 0.16. This conversion is useful in many real-world applications, as decimals are often easier to work with, especially in financial and scientific calculations.

It's important to remember that some fractions may result in a repeating decimal. In such cases, the division may not terminate, or you may notice a pattern in the digits after a certain point. However, in the example of \( \frac{4}{25} \), the division yields a terminating decimal.

Decimal to Percent Conversion

Once you have a fraction converted to a decimal, the next step is often to represent that value as a percent. The conversion from decimal to percent is quite simple—you multiply the decimal by 100. Multiplying by 100 effectively shifts the decimal point two places to the right, which is the same as 'per cent' or per one hundred.

Using our earlier example of 0.16, we can convert this decimal to a percent like so: \( 0.16 \times 100 = 16\% \). Whether you're dealing with finances, such as interest rates, or trying to understand statistics, being able to switch between decimals and percents will be incredibly valuable.

Basic Algebra

At the heart of converting fractions to decimals and decimals to percents lies basic algebra. Understanding the fundamental operations of algebra is key. It involves arithmetic operations on variables as well as numbers. In the context of our example, converting the fraction \( \frac{4}{25} \), we use division, which is one of the basic operations of algebra.

As for converting decimals to percents, multiplication is the algebraic operation we employ. The multiplication by 100 is an algebraic way to scale a number by a power of 10, which is a common practice in algebra for managing decimal places and percentages. Both of these simple algebraic operations are building blocks for more complex mathematical concepts taught later on in algebra courses. A solid grasp of these basics ensures a strong foundation for future math endeavors.