Problem 81 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 1.8 ? 180 \% $$

Step-by-Step Solution

Answer

The answer is \(=\)

Step 1: Convert percentage to decimal

Change 180% to a decimal by dividing by 100: \( \frac{180}{100} = 1.80 \)

Step 2: Compare the decimal numbers

Compare 1.8 and 1.80. They are the same, so the solution to the exercise is \(=\)

Key Concepts

Percentages

When dealing with percentages, it's important to understand that a percentage is a way to express a number as a part of 100. For example, 180% means 180 out of 100. To convert a percentage to a decimal, you simply divide by 100. This conversion helps when you want to perform calculations or comparisons with other numbers in decimal form.

Let's look at how to convert percentages to decimals step-by-step:

• Identify the percentage you want to convert (like 180%).
• Divide the percentage by 100 to get its decimal form (e.g., 180% becomes 1.80).

This is useful because it allows us to work with percentages in the same way as other numbers, making operations like addition or comparison much more straightforward.

Decimals

Decimals are a way to represent numbers between integers, using a decimal point. Understanding decimals is crucial for comparing numbers, especially when they result from converting percentages. When you have a number like 1.8, it represents a value between 1 and 2.

Here are some things to remember when working with decimals:

• The digits after the decimal point show tenths, hundredths, thousandths, etc.
• 1.8 is the same as 1.80, because the trailing zero does not affect the value of the decimal.
• Decimals allow for precise representation of a wide range of values, from very small to very large numbers, without using fractions.

Understanding these basics helps make calculation and comparison of values easier, especially when converting numbers from one form to another, like from percent to decimal.

Comparing numbers

Comparing numbers is determining the relationship between them, which is often about deciding if one number is greater than, less than, or equal to another. This is especially important in mathematics to validate relationships and perform accurate calculations.

When comparing numbers:

• Check if the numbers are the same by comparing digits, especially after conversion forms like percentages to decimals, as both 1.8 and 1.80 have identical values.
• When comparing decimals, align decimal points and compare each digit to determine equality or difference.

This exercise showcased comparing 1.8 and 1.80, and since these values are equal, the statement was completed with an equals sign (=). This reminds us of how decimals operate and the importance of accuracy in comparing numbers.