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Chapter 2: Problem 20

Write an integer for each situation. Then graph on a number line. $$12^{\circ}$ above zero$$

Short Answer

Expert verified
The integer is 12; plot it as a point on the number line at 12.

Step by step solution

01

Understand the Problem

The problem asks us to write an integer that represents the temperature situation "12 degrees above zero." To do this, we need to recall that temperatures above zero are positive integers.
02

Identify Integer Representation

Since "above zero" means a positive number, the integer representation of '12 degrees above zero' is simply 12.
03

Draw a Number Line

On a number line, draw a horizontal line and mark zero in the middle. We will need to count marks from 0 up to 12 on the right side.
04

Plot the Integer on the Number Line

Starting from 0, count 12 units to the right and mark it. Draw a dot above the 12 mark on the number line to represent 12 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Positive Integers
Positive integers are numbers that are greater than zero and without any fractional or decimal part. They are straightforward and commonly used in everyday situations, like counting objects or measuring temperatures above a base level. Hence, when we say a temperature is 12 degrees above zero, we use the integer 12 to express this.

Keep in mind that positive integers are found on the right-hand side of zero on a number line. They start from 1 and continue upwards to infinity. Here are some key things to remember about them:
  • They do not include zero.
  • They are always positive, meaning they do not have a negative sign in front of them.
  • Examples include 1, 2, 3, and so forth.
Number Line
A number line is a visual representation of numbers laid out in a straight horizontal line. It helps us visualize and solve problems involving different types of numbers, including positive integers.

The number line typically extends infinitely in both directions. However, we often focus on a segment of it to make observations or solve particular problems.

When graphing or solving a problem, like plotting a temperature of 12 degrees, a number line:
  • Starts with zero at some fixed point.
  • Has numbers increasing to the right, indicating positive values.
  • Has divisions or tick marks, which help in precisely locating numbers.
Number lines are essential in comprehending the concept of integers and their arrangements.
Graphing Integers
Graphing integers on a number line is a straightforward but powerful way to depict and understand their relationship with zero and other numbers. When we graph an integer, we visually place it on the number line according to its value.

For instance, to graph the integer 12 on a number line, you follow these steps:
  • Start at zero since it serves as the reference.
  • Move 12 units to the right because 12 is a positive integer.
  • Place a dot or mark above the number 12 to clearly indicate its position.
Graphing helps us see the difference and distance between integers, which is valuable for understanding arithmetic operations or gauging magnitude in context.

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