Problem 82 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 0.22 ? 20 \% $$

Step-by-Step Solution

Answer

The completed statement is \(0.22 > 20 \%\).

Step 1: Convert the Percentage to a Decimal

First, convert the percentage to a decimal. This can be done by dividing the percentage by 100. So, \(20\% = 20/100 = 0.20\) or 2/10.

Step 2: Compare the Values

Next, compare the decimal numbers. We can see that \(0.22\) is larger than \(0.20\), so the comparison symbol that fits this condition is \(>\).

Step 3: Write the Completed Statement

Putting the comparison symbol into the original statement, we get \(0.22 > 20 \%\).

Key Concepts

Percentage to Decimal Conversion

Understanding how to convert percentages to decimals is crucial when working with different types of numerical data. Simply put, a percentage represents a number out of 100. To transform a percentage into a decimal, divide the percentage by 100. This process effectively shifts the decimal point two places to the left.

For example, converting 20% to a decimal involves dividing 20 by 100, which gives us 0.20. It's a straightforward procedure: take the number (20), and since 'percent' means 'per hundred', you divide by 100 to get the decimal equivalent (\( \frac{20}{100} = 0.20 \) or 0.2). It's essential for students to grasp this concept as it forms the foundation for many mathematical calculations involving percentages.

Inequalities in Math

Inequalities are comparisons between two values that may not be equal. In math, we use symbols like < (less than), > (greater than), and = (equal to) to denote these relationships. Understanding inequalities allows us to make statements about the relative size of numbers.

When we say that one number is less than another, we use the < sign, pointing to the smaller number. Conversely, the > sign points to the larger number when one is greater than the other. The equal sign is used when two values are exactly the same. An easy tip to remember is that the symbol always 'eats' the larger number - so for 0.22 and 0.20, since 0.22 is larger, the correct inequality symbol would be >, making 0.22 > 0.20.

Decimal Numbers Comparison

Comparing decimal numbers is an extension of understanding place value. When comparing decimals, we start by looking at the highest place value (the digits furthest to the left) and compare each place value in sequence until we find a difference.

For example, with 0.22 and 0.20, both have 2 in the tenths place, but 0.22 has 2 in the hundredths place while 0.20 has 0. Since 2 is greater than 0, we can determine that 0.22 is the larger number. Always compare decimal places methodically from left to right to understand which decimal is larger, smaller, or if they are equal.