Rational Numbers and Converting Integers
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Questions and Answers

What is the set of numbers that includes whole numbers, their opposites, and 0, but excludes fractions and decimals?

Integers

What is the definition of a rational number?

A number that can be written as a ratio of integers, in the form A/B, where A and B are both integers, and B cannot be 0.

How can an integer be written as a fraction or decimal?

For example, 7 can be written as 7/1 or 0.875.

What is the absolute value of a number?

<p>The distance between a number and 0 on the number line.</p> Signup and view all the answers

How can you graph a rational number on a number line?

<p>Plot the point on the line and count the units from 0 to determine the absolute value.</p> Signup and view all the answers

How do you compare rational numbers with opposite signs?

<p>A positive number is always greater than a negative number.</p> Signup and view all the answers

What is the temperature closest to the freezing point of water (0°C) in a table of temperatures?

<p>The temperature with the smallest absolute value.</p> Signup and view all the answers

How do you determine the temperature farthest from 0°C in a table of temperatures?

<p>The temperature with the largest absolute value.</p> Signup and view all the answers

Which of the following is not a characteristic of an integer?

<p>It can be a fraction</p> Signup and view all the answers

What is the equivalent decimal representation of the integer 7?

<p>7.0</p> Signup and view all the answers

What is the absolute value of -5?

<p>5</p> Signup and view all the answers

How can you find the absolute value of a number on a number line?

<p>Count the units from 0 to the number</p> Signup and view all the answers

Which of the following is true when comparing rational numbers?

<p>A positive number is always greater than a negative number</p> Signup and view all the answers

What is the purpose of finding the absolute value of a temperature in a table of temperatures?

<p>To find the temperature closest to the freezing point of water</p> Signup and view all the answers

Which of the following is an example of a rational number?

<p>All of the above</p> Signup and view all the answers

What is the result of comparing the absolute values of two rational numbers?

<p>The number with the smaller absolute value is always less than</p> Signup and view all the answers

What is the advantage of using a number line to graph rational numbers?

<p>It helps to visualize the comparison of numbers</p> Signup and view all the answers

What is the relationship between the absolute value of a number and its position on a number line?

<p>The absolute value is the distance from 0, regardless of direction</p> Signup and view all the answers

Study Notes

Integers and Rational Numbers

  • Integers: the set of whole numbers and their opposites, including 0, positive numbers, and negative numbers, but no fractions or decimals.
  • 0 is neither positive nor negative.
  • Rational numbers: numbers that can be written as a ratio of integers, in the form A/B, where A and B are both integers, and B cannot be 0.

Converting Integers to Fractions or Decimals

  • An integer can be written as a fraction or decimal, e.g., 7 = 7/1 or 0.875.
  • Fractions and decimals are equivalent representations of rational numbers.

Absolute Value

  • Absolute value: the distance between a number and 0 on the number line.
  • The absolute value of a number is always positive.
  • The absolute value of a number is the distance from 0 to the number on the number line, regardless of the direction (positive or negative).

Graphing Rational Numbers on a Number Line

  • A number line can be used to visualize and compare rational numbers.
  • To graph a rational number on a number line, plot the point on the line and count the units from 0 to determine the absolute value.
  • The absolute value of a number can be found using the number line, without actually drawing the line.

Comparing Rational Numbers

  • To compare rational numbers, read the comparison statement from left to right.
  • Use the symbols < (less than), > (greater than), and = (equal to) to compare numbers.
  • When comparing numbers with opposite signs, a positive number is always greater than a negative number.
  • Use the absolute value of a number to compare it to another number, regardless of sign.

Practical Example: Temperature Comparison

  • A table of temperatures in degrees Celsius can be compared using absolute values and number lines.
  • The temperature closest to the freezing point of water (0°C) is the one with the smallest absolute value.
  • The temperature farthest from 0°C is the one with the largest absolute value.

Integers and Rational Numbers

  • Integers include whole numbers, their opposites, and 0, but exclude fractions and decimals.
  • 0 is neither positive nor negative.
  • Rational numbers are numbers that can be expressed as a ratio of integers, i.e., A/B, where A and B are integers and B ≠ 0.

Converting Integers to Fractions or Decimals

  • Integers can be written as fractions or decimals, e.g., 7 = 7/1 or 0.875.
  • Fractions and decimals are equivalent representations of rational numbers.

Absolute Value

  • Absolute value is the distance between a number and 0 on the number line.
  • The absolute value of a number is always positive.
  • The absolute value of a number is the distance from 0 to the number on the number line, regardless of direction (positive or negative).

Graphing Rational Numbers on a Number Line

  • A number line can be used to visualize and compare rational numbers.
  • To graph a rational number, plot the point on the line and count the units from 0 to determine the absolute value.
  • The absolute value of a number can be found using the number line without drawing the line.

Comparing Rational Numbers

  • Compare rational numbers by reading from left to right.
  • Use <, >, and = to compare numbers.
  • A positive number is always greater than a negative number when comparing numbers with opposite signs.
  • Use absolute value to compare numbers, regardless of sign.

Practical Example: Temperature Comparison

  • Use absolute values and number lines to compare temperatures in degrees Celsius.
  • The temperature closest to 0°C has the smallest absolute value.
  • The temperature farthest from 0°C has the largest absolute value.

Integers and Rational Numbers

  • Integers include whole numbers, their opposites, and 0, but exclude fractions and decimals.
  • 0 is neither positive nor negative.
  • Rational numbers are numbers that can be expressed as a ratio of integers, i.e., A/B, where A and B are integers and B ≠ 0.

Converting Integers to Fractions or Decimals

  • Integers can be written as fractions or decimals, e.g., 7 = 7/1 or 0.875.
  • Fractions and decimals are equivalent representations of rational numbers.

Absolute Value

  • Absolute value is the distance between a number and 0 on the number line.
  • The absolute value of a number is always positive.
  • The absolute value of a number is the distance from 0 to the number on the number line, regardless of direction (positive or negative).

Graphing Rational Numbers on a Number Line

  • A number line can be used to visualize and compare rational numbers.
  • To graph a rational number, plot the point on the line and count the units from 0 to determine the absolute value.
  • The absolute value of a number can be found using the number line without drawing the line.

Comparing Rational Numbers

  • Compare rational numbers by reading from left to right.
  • Use <, >, and = to compare numbers.
  • A positive number is always greater than a negative number when comparing numbers with opposite signs.
  • Use absolute value to compare numbers, regardless of sign.

Practical Example: Temperature Comparison

  • Use absolute values and number lines to compare temperatures in degrees Celsius.
  • The temperature closest to 0°C has the smallest absolute value.
  • The temperature farthest from 0°C has the largest absolute value.

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Description

Learn about integers, rational numbers, and how to convert integers to fractions or decimals. Understand the basics of whole numbers, positive and negative numbers, and ratios.

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