Problem 60 - Algebra A Combined Function

Question

Write each percent as \(a\) decimal. $$ 36 \% $$

Step-by-Step Solution

Answer

36% is written as 0.36.

Step 1: Understand the Percent

A percent is a way of expressing a number as a fraction of 100. The symbol '%' means 'per hundred'. So, 36% means 36 out of 100.

Step 2: Convert Percent to Fraction

Convert 36% directly to a fraction: \[ \frac{36}{100} \]. This fraction represents the same value as the percent.

Step 3: Simplify Fraction (if necessary)

Check if the fraction \( \frac{36}{100} \) can be simplified. However, for the purpose of converting to a decimal, it's more useful to leave it in this form.

Step 4: Convert Fraction to Decimal

Divide the numerator by the denominator to find the decimal equivalent: \( 36 \div 100 = 0.36 \).

Step 5: Conclusion

Thus, 36% can be expressed as the decimal 0.36.

Key Concepts

Understanding Percentages

Percentages are a fundamental concept in mathematics, often used to express a proportion or a part of a whole. The term 'percent' literally means "per hundred." For example, 36% (pronounced as thirty-six percent) indicates 36 parts out of 100. This representation makes it easier to visualize and compare different ratios at a glance. When you see a percentage, always think of it as a part of a hundred. They are helpful in a variety of real-world applications, like calculating tips, sales tax, or even in statistics.

Decimals Explained

Decimals are another method to represent numbers that are not whole. They are based on the concept of decimal notation, which stands on the powers of ten. Unlike fractions, decimals provide a way to express values as a continuous entity, making them more flexible in calculations involving division, multiplication, and comparison. For example, the decimal 0.36 represents the same value as the percentage 36%. It tells us that there are 36 hundredths in the number.

The Role of Fractions

Fractions depict numbers as parts of a whole, composed of a numerator and a denominator. The numerator denotes how many parts are being considered, while the denominator indicates the total number of equal parts. For instance, the fraction \( \frac{36}{100} \) describes 36 parts of a whole that is divided into 100 equal portions. Fractional representation is crucial in various mathematical computations. It's especially useful in shows the relationship between the numerator and denominator, giving insight into proportions and comparisons.

Steps for Conversion

Converting from percent to decimal is simple with a straightforward method:

• Step 1: Recognize that the percent is a fraction of 100. So, 36% is \( \frac{36}{100} \).
• Step 2: Note if the fraction can be further reduced. However, it’s generally converted directly for decimal conversion.
• Step 3: To move from fraction to decimal, divide the numerator by the denominator. Here, \( 36 \div 100 = 0.36 \).
• Conclusion: The percent 36% is now expressed as the decimal 0.36. This easy process is key for many mathematical applications.

Bringing it all together, these steps help convert percentages into decimals smoothly, ensuring you understand both representations.