Problem 88 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 5 \% ? 0.5 $$

Step-by-Step Solution

Answer

5% < 0.5

Step 1: Convert Percentage to Decimal

In order to compare '5%' with '0.5', convert the '5%' to decimal. The way to convert a percentage into a decimal is by dividing it by 100. So, \(5\% = \frac{5}{100} = 0.05\)

Step 2: Compare the Numbers

Now, compare 0.05 (the decimal equivalent of '5%') to 0.5. Since 0.05 is less than 0.5, the symbol '<' fits in the blank.

Key Concepts

Percentage to Decimal Conversion

Understanding how to convert percentages to decimals is fundamental in making accurate comparisons in mathematics. It's quite straightforward: a percentage represents a number out of 100. Therefore, converting a percentage to a decimal simply involves dividing the percentage by 100. For example, to convert 5% to a decimal, divide 5 by 100 which results in 0.05.

Here's a quick guide to help you:

• Drop the percentage (%) sign: Take the number without the '%'.
• Divide by 100: Move the decimal point two places to the left.
• If necessary, pad with zeros: Ensure the number has two decimal places, adding zeros if needed.

This process is invaluable when trying to compare a percentage value with other numerical expressions, like decimals or other percentages.

Inequalities with Decimals

Working with inequalities requires a strong grasp of how to accurately compare decimal numbers. Inequalities use symbols to indicate the relative size of two numbers. When comparing decimals, consider the following:

• Compare place values from left to right, starting with the largest (usually the place before the decimal for non-negative numbers).
• If the digits are the same, move one place to the right until you find a difference.
• Don't forget to include zeros that can impact the comparison materially.

When comparing 0.05 to 0.5, it's clear that 0.5 has a '5' in the tenths place, whereas 0.05 has a '0' in the tenths place and a '5' in the hundredths place. Hence, 0.05 is less than 0.5, illustrated by the inequality 0.05 < 0.5.

Mathematical Comparison Symbols

Comparison symbols are the shorthand of mathematics used to show the relationship between two values. The most common symbols include less than (<), greater than (>), and equals (=).

An easy way to remember these symbols is:

• The symbol '<' means the number on the left is smaller than the number on the right.
• The symbol '>' means the number on the left is larger than the number on the right.
• The symbol '=' means the numbers on either side are exactly the same.

These symbols are cornerstones in math, allowing for succinct communication of comparison results. In the example given, we use the '<' symbol to demonstrate that 5% (which was converted to 0.05 decimal) is indeed less than 0.5.