Question

\begin{tabular}{|l|l|} \hline\(-11.954 \ldots 11.945\) \\ \hline Select... & \\ \hline\(>\) \\ \hline\(<\) \\ \hline & \\ \hline \end{tabular}

Short answer

-11.954 < 11.945

Step-by-step solution

- Identify the Numbers

Look at the two numbers given in the problem: -11.954 and 11.945.

- Compare the Signs

Notice that -11.954 is a negative number and 11.945 is a positive number. In general, negative numbers are always less than positive numbers.

- Select the Correct Inequality Symbol

Based on the signs of the numbers, -11.954 is less than 11.945. Therefore, the correct inequality symbol to use is <.

Key concepts

negative numbers

Negative numbers play an essential role in mathematics. They are numbers less than zero, often representing a loss, decrease, or a value below a certain standard. Negative numbers are denoted by a minus sign (-) before the number. For example, in the exercise '-11.954', the negative sign in front of 11.954 makes it a negative number. When we compare negative numbers to positive ones, the negative numbers are always smaller. For example, -1 is less than 1, -10 is less than 5, and in our given exercise, -11.954 is less than 11.945. Remember, the further a negative number is from zero, the smaller its value.

positive numbers

Positive numbers are numbers greater than zero. They represent quantity, gain, or a value above zero. They do not have any prefix sign, but we often write a '+' sign to denote positivity, especially for clarity in some contexts. In the exercise, 11.945 is a positive number. Comparing positive numbers with negative numbers is straightforward because positive numbers are always greater than negative numbers. For instance, 5 is greater than -2, and 11.945 is greater than -11.954. Recognizing positive numbers and their comparison to negative numbers is fundamental in understanding and solving inequalities.

mathematical reasoning

Mathematical reasoning involves making sense of mathematical concepts and arriving at logical conclusions. In the given exercise, we use reasoning to compare -11.954 and 11.945. Here's a breakdown of the reasoning process:

• Identify the Numbers: Recognize that we are comparing -11.954 and 11.945.
• Compare the Signs: Note that -11.954 is negative and 11.945 is positive.
• Apply the Rule: Remember that a negative number is always less than a positive number.
• Select the Correct Inequality: Since -11.954 is less than 11.945, we use the '<' symbol.

This logical process allows us to determine that the correct statement is -11.954 < 11.945. Developing strong mathematical reasoning skills helps in solving problems accurately and efficiently.