Problem 58 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$\frac{1}{5}$$

Step-by-Step Solution

Answer

20%

Step 1: Convert Fraction to Decimal

Begin by converting the fraction \( \frac{1}{5} \) to a decimal. To do this, divide the numerator (1) by the denominator (5), resulting in 0.2.

Step 2: Convert Decimal to Percent

Next, convert the decimal obtained (0.2) into a percentage. Multiply the decimal by 100: 0.2 \( \times \) 100 = 20. This means the fraction \( \frac{1}{5} \) is equivalent to 20%.

Step 3: Conclusion

The fraction \( \frac{1}{5} \) converts to 20% when expressed as a percentage.

Key Concepts

Fraction to Decimal Conversion

Fractions are numbers that represent a part of a whole. To convert a fraction into a decimal, you need to carry out division. You take the numerator, which is the top number of the fraction, and divide it by the denominator, the bottom number.
For instance, with the fraction \( \frac{1}{5} \), the numerator is 1, and the denominator is 5. By dividing 1 by 5, you get the decimal 0.2.
Understanding this process is important because it helps you see fractions in a form that's often easier to handle in calculations and real-life applications. Remember, dividing smaller numbers by larger numbers can often result in a decimal that's less than 1 which is a vital point to note.

Decimal to Percent Conversion

Converting a decimal to a percent is a simple yet powerful skill. Percentages are just another way to express fractions and decimals in a more relatable, everyday format. To convert a decimal into a percent, you multiply it by 100.
For example, when you have a decimal like 0.2, multiplying by 100 shifts the decimal point two places to the right, changing it to 20%.
This makes sense because 'percent' literally means 'per 100', so you are finding how many parts per 100 the decimal represents. Converting to a percent is a great way to express how much of something you have or need, in terms that are easy to understand and compare.

Arithmetic Operations

Arithmetic operations are the basic calculations we perform with numbers, including addition, subtraction, multiplication, and division. These operations are the building blocks of mathematics and are crucial for carrying out conversions.
In the context of converting fractions to decimals, division is the key operation you use. You are dividing the numerator by the denominator to convert a fraction into a decimal format.
When converting decimals to percentages, multiplication becomes essential as you multiply by 100. These arithmetic skills allow us to change numbers from one form to another, solving real-world problems more easily. Understanding these will empower you to handle many mathematical scenarios almost anywhere you encounter numbers.