Put rational numbers in order

Key Notes:

1. Understanding Rational Numbers:

  • A rational number is any number that can be expressed as a fraction a/b​, where aaa and b are integers, and b≠0.
  • Rational numbers include integers, fractions, decimals, and mixed numbers (both positive and negative).

2. Types of Rational Numbers:

  • Positive Rational Numbers: Numbers greater than zero (e.g., 3/4, 2, 0.75).
  • Negative Rational Numbers: Numbers less than zero (e.g., −5/8​, -3, -1.2).
  • Zero: Neither positive nor negative, but it is considered a rational number.

3. Converting Fractions and Decimals:

  • Sometimes it’s easier to compare and order rational numbers if they’re all in the same form (either fractions or decimals).
  • Convert fractions to decimals by dividing the numerator by the denominator.
  • Convert decimals to fractions (e.g., 0.5 = 1/2​).

4. Steps to Put Rational Numbers in Order:

Step 4: Use a number line if necessary to visually arrange the numbers.

Step 1: Convert all numbers to the same form (preferably decimals).

Step 2: If comparing fractions, find a common denominator.

Step 3: Compare the values from least to greatest (ascending order) or greatest to least (descending order).

Learn with an example

🗼 Put these numbers in order from least to greatest.

  • – 0.5
  • 0.1
  • – 5
  • You want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them first.
  • When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers.–5 is less than–0.5.
  • Next come the positive numbers. 0.1 is the only positive number. It is the greatest number in the list.
  • The numbers, written as decimals, in order from least to greatest are:
  • – 5
  • – 0.5
  • 0.1

🗼Put these numbers in order from least to greatest.

  • – 8 3/30
  • 8
  • – 8 2/10
  • First, write all the numbers as decimals.
  • -8 3/30=-8.1
  • -8 2/10=-8.2
  • You want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them first.
  • When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers. -8.2 is less than -8.1.
  • Next come the positive numbers. 8 is the only positive number. It is the greatest number in the list.
  • The numbers, written as decimals, In order from least to greatest are:
  • – 8.2 < – 8.1 <8
  • So, the correct answer is:
  • – 8 2/10
  • – 8 3/30
  • 8

🗼 Put these numbers in order from greatest to least.

  • – 3
  • 12 / 15
  • – 3 3 / 15
  • First, write all the numbers as decimals.
  • 12 / 15 = 0.8
  • -3 3 / 15 = -3.2
  • You want to order the numbers from greatest to least. Since positive numbers are greater than negative numbers, start with them first.
  • 0.8 is the only positive number. It is the greatest number in the list.
  • Next come the negative numbers, when comparing negative numbers, smaller numbers (If you Ignore the minus sign) are greater than larger numbers. -3 is greater than -3.2.
  • The numbers, written as decimals, in order from greatest to least are:
  • 0.8 > -3 > -3.2
  • So, the correct answer is:
  • 12 / 15
  • – 3
  • – 3 3 / 15

Let’s practice!🖊️