Problem 50 - Prealgebra

Question

Write as a percent. $$0.15$$

Step-by-Step Solution

Answer

0.15 as a percent is 15%.

Step 1: Understand the Decimal

Analyzing the number 0.15, we recognize that it is expressed in decimal form and needs conversion to percentage form. The numeral to the right of the decimal point represents hundredths.

Step 2: Convert to Percentage

To convert a decimal to a percentage, multiply the decimal by 100. This method moves the decimal point two places to the right, effectively converting a part of a whole into a whole number percentage.

Step 3: Perform the Conversion

Multiplying 0.15 by 100 gives us: \[0.15 \times 100 = 15\]Thus, 0.15 in percentage form is 15%.

Key Concepts

Decimal to Percent

Converting decimals to percentages might seem confusing at first, but it's a straightforward process once you understand it. Imagine you have a decimal like 0.15. This number denotes a fraction of a whole, specifically it represents 15 out of 100 when thought of as parts of a whole. To express this relationship in percent form, you multiply the decimal by 100. This multiplication shifts the decimal point two places to the right, transforming the decimal into a percentage. For instance, in our example, multiplying 0.15 by 100 gives us 15, which means 0.15 is equivalent to 15%.

This method is a quick and effective way to convert any decimal to a percentage, but it's important to remember to always multiply by 100 to get the correct percent form.

Mathematical Conversion

Understanding mathematical conversion is essential in mathematics, and changing decimals to percentages is a classic example of this. The core idea behind conversions is to express one mathematical value in another form without changing its actual worth or significance.

When converting a decimal, like 0.15, to a percentage, you're simply using the function of multiplication by 100 to shift the point and adjust the scale. This does not alter the inherent value but makes it suitable for presentation in a different format, often more relatable in everyday scenarios. By multiplying by 100, you are adhering to a universal scale, making it easy to compare quantities and grasp ratios.

Converting decimals to percentages is just one type of conversion, and being familiar with these processes can prove invaluable, not just in math, but in real-world applications such as finance, science, and data analysis.

Understanding Decimals

Decimals are a way to express fractions in a linear, base-10 system, offering a method to represent parts of a whole more succinctly. In essence, any decimal number is an expression of division by powers of ten. For example, 0.15 can be interpreted as 15 parts out of 100, aligning with the basic structure of our number system.

Decimals are positioned by place value:

• The first digit to the right of the decimal point is tenths (1/10).
• The second is hundredths (1/100), and this pattern continues.

These positions illustrate how to read and interpret decimals when you see them. Recognizing these positions helps in operations like addition, subtraction, or, as in our exercise, converting them to other forms like percentages.

Deepening your understanding of how decimals work prepares you for more complex mathematical concepts and practical applications, and empowers you to tackle questions such as changing them into percentages with confidence.