Problem 58 - Algebra 1

Question

Write the percent as a decimal. $$ 19.5 \% $$

Step-by-Step Solution

Answer

The decimal equivalent of \(19.5\% \) is 0.195.

Step 1: Understand percentage as a fraction

It is important to keep in mind that a percentage is fundamentally a fraction out of 100. That means, when we read \(19.5\% \), it can be understood as \(\frac{19.5}{100}\).

Step 2: Convert percentage to decimal

To convert a percentage into a decimal, we simply divide the percentage by 100. Therefore, \(19.5\% \) as a decimal will be \(\frac{19.5}{100} = 0.195\).

Key Concepts

Percent to Decimal Conversion

When tackling the conversion from percent to decimal, the crucial fact to grasp is that 'percent' means 'per hundred'. For instance, 19.5% is actually 19.5 per hundred. To convert a percentage to a decimal, you divide it by 100.

For example, converting 19.5% to a decimal involves doing the following calculation: \[\frac{19.5}{100} = 0.195\] Hence, 19.5% is equivalent to 0.195 in decimal form. It's simple once you remember this easy step - divide the percent value by 100, and you are done!

Percent as Fraction

Every percent can also be represented as a fraction. The denominator of this fraction is always 100, which consistently reflects the meaning of percentage being out of one hundred. So when you see 19.5%, you can immediately rewrite it as a fraction: \[\frac{19.5}{100}\].

This understanding is helpful not only for conversion to decimals but also while performing other mathematical operations. With 19.5% as \[\frac{19.5}{100}\], this form can be used in more complicated algebraic expressions as well.

Decimal Representation

Decimal representation means expressing numbers with a decimal point. This way of writing numbers is especially useful when dealing with parts of a whole. In the context of percentages, once you convert a percent to a decimal, you're showing the value as a part of one, not one hundred.

For instance, 19.5% becomes 0.195, and this decimal is less than one, indicating it is a part of a whole. Decimals are convenient for calculations and are preferred in most mathematical and real-world applications like measuring, currency, and computing.

Algebraic Operations

Understanding how to convert percentages and fractions to decimals is fundamental to algebra. This skill is crucial as it allows you to perform algebraic operations like addition, subtraction, multiplication, and division with these numbers.

For example, if you have to add 19.5% of a number to another number, converting that percent to 0.195 as a decimal is your first step. You'd then multiply the first number by 0.195 to find out how much to add to the second number. Therefore, mastering these conversions paves the way for tackling more complex algebra problems.