Problem 25 - Prealgebra

Question

Express each percent as a fraction or mixed number in simplest form and as a decimal. $$61 \%$$

Step-by-Step Solution

Answer

61% equals \( \frac{61}{100} \) as a fraction and 0.61 as a decimal.

Step 1: Convert Percent to Fraction

To express 61% as a fraction, recall that a percent is a way to express a number out of 100. So, 61% is equivalent to \( \frac{61}{100} \). This fraction is already in its simplest form as both 61 and 100 have no common factors other than 1.

Step 2: Convert Percent to Decimal

To convert 61% to a decimal, divide the percentage by 100. This can be done by moving the decimal point two places to the left. So, \( 61\% \) becomes 0.61 when converted to a decimal.

Key Concepts

Percent to Decimal

When you want to convert a percent to a decimal, you're essentially transforming a number out of one hundred into its base ten format. The word "percent" means "per one hundred," which offers a clue on how to proceed. To switch from percent to decimal:

• Simply divide the percent by 100.
• Imagine moving the decimal point two places to the left.

For example, with 61%, dividing by 100 or moving the decimal point two spots left converts it into 0.61. This process works universally, regardless of how large or small the percentage is. If you have a calculator handy, you can quickly verify your result by performing the division directly.

Simplifying Fractions

Simplifying fractions is the process of reducing the fraction to its lowest terms. A fraction is considered simplified when the numerator (top number) and the denominator (bottom number) are as small as possible, sharing no common factors except for 1. Here's how you can simplify fractions easily:

• Find the greatest common factor (GCF) of both the numerator and the denominator.
• Divide both terms of the fraction by this GCF.

In the case of 61% represented as a fraction \( \frac{61}{100} \), it is already as simple as it gets. The numbers 61 and 100 do not share any common factors apart from 1. Thus, it remains \( \frac{61}{100} \).

Division

Division is a mathematical operation where you are splitting a number into equal parts. In the context of percentages, division is regularly used to convert percentages to their fractional or decimal equivalents. For instance, when converting from percent to decimal, you're instructed to "divide by 100". Here's how division helps:

• It allows recalibrating percentages into base ten or a fractional form.
• Understanding division simplifies the concept of percents relating to everyday quantities, be it discounts, interest rates, or data analysis.

Knowing how to correctly use and apply division makes managing percentages a breeze, and it's crucial for many applications in both educational settings and practical, real-world scenarios.

Converting Percentages

Converting percentages, whether into fractions or decimals, is an essential skill. A percentage itself represents a ratio where the base is always 100. Learning to convert these into fractions or decimals is important for several reasons:

• It helps in visualizing and assessing the size of different parts relative to a whole.
• Empowers you in multiple areas including finance, science, and statistics.
• Fosters a better understanding of how quantities relate to each other.

When you convert 61% to \( \frac{61}{100} \) as a fraction and 0.61 as a decimal, it showcases how the percentage can communicate data in different but equally valuable forms depending on the context.