Problem 87 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 1 \% ? 0.1 $$

Step-by-Step Solution

Answer

1% < 0.1

Step 1: Convert Percentage to Decimal

The first step is to convert 0.1 to a percentage. 0.1 in decimal form is equal to 10% in percentage form.

Step 2: Consider the numerical values

Next, simply compare the two percentages: 1% and 10%. This should lead to the conclusion that 1% is less than 10%.

Step 3: Identify the correct relational symbol

Finally, capture the outcome of the comparison in the appropriate mathematical symbol. As 1% is less than 10%, the correct symbol to use is \(<\).

Key Concepts

Percentage to Decimal Conversion

Understanding how to convert percentages to decimals is an essential step in comparing numerical values. To convert a percentage into a decimal, you will need to divide the percentage by 100. This is because the term 'percent' essentially means 'per one hundred'. An easy way to remember this is to think of the percent sign ('%') as 'over one hundred'.

For instance, to convert 1% to a decimal, simply divide 1 by 100, which yields 0.01. Similarly, when converting 10%, divide 10 by 100, resulting in 0.10. This process is crucial as it allows for direct comparisons when handling different formats of numbers—like when you compare percentages and decimals directly.

Mathematical Comparison Symbols

Mathematical comparisons involve determining the relative size of two numbers. To depict these relationships, we use comparison symbols which are fundamental in conveying mathematical expressions. The three primary symbols used for this purpose are '<' for less than, '>' for greater than, and '=' for equal to.

When you see the symbol '<', it indicates that the number on the left side is smaller than the number on the right. Conversely, the '>' symbol means the number on the left is larger. If two numbers are the same, we use the equality sign '='. These symbols are critical for efficiently communicating the results of numerical comparisons, both in mathematical practice and in everyday contexts.

Numerical Value Comparison

When comparing numerical values, the focus is on understanding which of the two numbers is larger, smaller, or whether they are equal. After converting all numbers to the same format, as we would with percentage to decimal conversion, we examine their values. It's like sizing up two objects to determine which one takes up more space.

In our exercise, after converting both numbers to percentages, we compare 1% and 10%. Here, it's clear that 1% is smaller than 10%. This understanding of numerical comparison guides us in choosing the correct mathematical comparison symbol to express the relationship between two figures clearly and effectively.