Problem 85 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=.\) $$ 0.3 ? 33 \% $$

Step-by-Step Solution

Answer

The correct completion of the statement is 0.3 < 33%.

Step 1: Convert Percentage to Decimal

In order to compare the given decimal number with the percentage, they need to be in the same format. So, convert the percentage (33%) into a decimal. To do this, move the decimal point two places to the left, getting 0.33.

Step 2: Compare the Decimal Values

Now that both numbers are in decimal format (0.3 and 0.33), the comparison can be performed. Comparing these, it can be seen that 0.3 is less than 0.33.

Step 3: Insert the Correct Symbol

Having found that 0.3 is less than 0.33, insert the correct symbol, which is '<', to complete the statement.

Key Concepts

Convert Percentage to Decimal

When you come across a percentage in a math problem, it's often necessary to convert it into a decimal. This is because decimals and percentages need to be in the same format for easy comparison or calculation. To convert a percentage to a decimal, simply move the decimal point two places to the left. For instance, to convert 33% to a decimal, move the decimal point two slots from its end position, turning the percentage into 0.33. This easy step ensures that you can work with percentages in the same way as decimals, allowing for seamless calculations and comparisons. Remember, this rule applies to all percentages, whether large or small.

Inequality Symbols

Inequality symbols are essential when comparing numbers or expressions in mathematics. The most common inequality symbols are:

• '<': Represents 'less than'.
• '>': Represents 'greater than'.
• '=': Represents 'equal to'.

These symbols help in determining and expressing the relationship between two values. For example, when comparing the two decimal values 0.3 and 0.33, the '<' symbol is used because 0.3 is less than 0.33. Familiarizing yourself with inequality symbols not only helps in mathematical expressions but also in solving various real-world problems where a comparison is required. Pay attention to the direction of the inequality symbol, as it can entirely change the meaning of the statement!

Compare Decimal Values

Comparing decimal values is a crucial skill in math, especially when dealing with both decimals and percentages. Start by ensuring all values are in decimal form. When comparing two decimals, observe their digits place by place, starting from the left.

Take 0.3 and 0.33 as an example:

• First, compare the digit in the tenths place. Here, both have a '3', so they are equal at this level.
• Next, compare the hundredths place. 0.3 has no additional digit here, effectively being 0, while 0.33 has a '3'.

With 0.33 having a larger digit in the hundredths place, it's clear that 0.3 is less than 0.33. This step-by-step approach helps ensure accurate comparisons and the correct use of inequality symbols. This methodology is beneficial not only in academic settings but also in practical, everyday calculations such as financial assessments.