Problem 50 - Algebra 1: Concepts and Skills

Question

Compare using \(<,>,\) or \(=\). \(25 \% ? 0.25\)

Step-by-Step Solution

Answer

25% = 0.25

Step 1: Understand the conversion between percentages and decimal numbers

A percentage is just another way to express a fraction with a denominator of 100. To convert a percentage to a decimal, the percentage sign (%) needs to be removed and the number is then divided by 100. Therefore, 25% can be converted to a decimal by removing the percentage sign and dividing by 100, and that equals 0.25.

Step 2: Compare the two numbers

Now that both numbers are in decimal form, we can compare them directly. In this case, 0.25 (converted from 25%) and 0.25 are exactly equal.

Key Concepts

Percentage to Decimal Conversion

To understand mathematics, one must often switch between different forms of representing numbers. An essential skill is converting a percentage to a decimal. This process is straightforward: simply remove the percentage sign ( ) and then divide the number by 100. For example, to convert 25% to a decimal, you would drop the and perform the division: 25 ÷ 100, which equals 0.25.

Why do we divide by 100? This is because 'per cent' means 'per hundred,' so you are effectively calculating how many 'parts out of 100' the percentage represents. Converting percentages to decimals is a fundamental step in various mathematical calculations and is vital for comparing numerical values when they are expressed differently.

Comparing Numbers

Comparing numbers to determine their relative size is a daily exercise in math classes. When you are given two numbers, regardless of how they are presented, you can compare them using mathematical symbols for 'less than' ( ), 'greater than' ( ), or 'equal to' ( = ).

If both numbers are already in decimal form, the comparison is simple. You look at these decimals place by place, starting from the leftmost digit. If the numbers are in different formats, such as one number is a percentage and the other is a decimal, you must first convert them to a common format. This makes it easier to see which is larger, smaller, or if they are equal. Avoid common mistakes by ensuring you convert carefully and check your work.

Mathematical Expressions

A mathematical expression is a combination of numbers, variables, and operations that represent a particular quantity or idea. To solve problems involving expressions, it's important to understand the rules and properties of math operations such as addition, subtraction, multiplication, and division.

When dealing with percentages and decimals, recognizing how these expressions can be transformed from one form to another is crucial. It allows you to simplify and solve problems accurately. Mathematical expressions are not just about calculations; they are the language of mathematics that enables us to represent and solve a wide range of real-world problems.