Problem 6 - Algebra A Combined Function

Question

Insert \(<,>,\) or \(=\) in the space between the paired numbers to make each statement true. $$ \begin{array}{ll} 1.13 & 1.13 \end{array} $$

Step-by-Step Solution

Answer

The correct symbol is \(=\).

Step 1: Understanding the Symbols

The symbols \(<\), \(>\), and \(=\) are used to compare two numbers. \(<\) means less than, \(>\) means greater than, and \(=\) means equal.

Step 2: Compare the Whole Numbers

Look at the whole numbers on either side of the space. In this case, both numbers are 1, which means they are equal.

Step 3: Compare the Decimal Parts

Compare the digits after the decimal point. Both sides have .13, and since 13 is equal to 13, the decimal parts are also equal.

Step 4: Combine Your Findings

Since both the whole numbers and the decimal parts are equal, the entire numbers are equal. Therefore, we place an \(=\) symbol between them.

Key Concepts

Inequality Symbols

Inequality symbols are used in mathematics to compare the size or order of two numbers.These symbols include:

• \(<\) : This symbol means "less than." It is used when the number before is smaller than the number after it.
• \(>\) : This symbol signifies "greater than." It is used when the number before it is larger than the one after it.
• \(=\) : The equal sign indicates that two numbers are the same in value.

For example, in comparing 3 and 5, the correct symbol to use is \(<\) because 3 is less than 5: 3 \(<\) 5. Understanding these symbols is essential as they help in describing and analyzing relationships between numbers in math.

Decimal Comparison

When comparing decimal numbers, it's important to consider both the whole number and the decimal parts separately. Decimals are numbers that have a fractional part, represented by digits following a dot (.). Here’s how you can compare decimal numbers effectively:

• **Whole Number Comparison:** Check the whole number part first. If they are different, decide with the inequality symbols based on their size.
• **Decimal Part:** If the whole numbers are equal, move on to compare the decimal parts.Compare the numbers starting from the tenths place, then hundredths, and so on until a difference is found.

In a situation like comparing 1.13 and 1.15, the whole numbers are the same. However, looking at the decimal parts, 0.13 is less than 0.15, so the correct comparison would be 1.13 \(<\) 1.15. Decimal comparison helps ensure precision, especially in measurements and scientific calculations.

Whole Numbers

Whole numbers are a set of numbers that include all natural numbers (non-negative numbers) without fractions or decimals. They start from 0, 1, 2, and continue infinitely upwards. Here’s why they are important in number comparison:

• **Basic Value Comparison:** Whole numbers represent the value without any fractional part, making them easy to compare directly.
• **Simplicity in Order:** Since they lack decimals, comparing whole numbers is straightforward – simply check which number is larger or smaller.

For instance, when comparing 2 and 5, we can easily say that 2 \(<\) 5 as 2 is less than 5. Whole numbers form the basis of our number system and play a critical role in everyday math applications.