Ordering Rational Numbers

Ordering Rational Numbers – Definition

Rational numbers include all integers, fractions and decimals that can be expressed as a fraction of two integers, where the denominator is not zero.

Before you begin this learning text about ordering rational numbers, make sure you are familiar with Decimals Greater than 1 as Fractions, Ordering Fractions on a Number Line, and Comparing Decimals on a Number Line: Up to Thousandths as all of these topics are crucial for understanding how to order rational numbers.

To order rational numbers, we need to compare their sizes. This can sometimes be tricky, especially with fractions and decimals, but don't worry, we've got some easy methods to follow!

Comparing Rational Numbers – Methods

• Comparing Whole Numbers: This is straightforward. Larger numbers are greater (e.g., 5 is greater than 3). Use the place value of the digits of a number to compare them. This is particularly helpful in very big or very small numbers.

• Comparing Fractions: To compare fractions, they must have the same denominator. If they don’t, you will need to find their equivalent fractions that do have the same denominator. Then, the fraction with the larger numerator is greater.

• Comparing Decimals: Line up the decimal points and compare digits from left to right, as the value of the digits from left to right decreases with each place value we move along (5 hundreds is a greater value than 5 tens). The first different digit determines which is greater or smaller based on the value of the digit. Placing the decimal number on a place value chart can be helpful for understanding which digit represents 10ths, 100ths, 1000ths etc.

• Comparing Fractions and Decimals: Convert them to the same type (either both fractions or both decimals) and then compare them as usual. View the video on Decimals Greater than 1 as Fractions to get an idea of how this can work.

To order rational numbers, you can follow these steps:

Common Fractions and Equivalent Decimals

Here is a table you can reference that shows some commonly used fractions and their decimal equivalents. This is not a complete list, and you can copy this and add any additional ones you know of!

Ordering Rational Numbers – Detailed Examples

Now, let's try some examples together. Pay close attention to each step.

Order these rational numbers from smallest to largest: 4, $\frac{5}{2}$, 2.3

Convert numbers: $\frac{5}{2}$ as a decimal is 2.5.

Understand the Relationship: Notice that $\frac{5}{2}$ is 2.5, which is greater than 2.3, but less than 4.

Order the Numbers: Since 2.3 is less than 2.5, and both are smaller than 4, the order is 2.3, 2.5, 4.

Convert to Original Expressions: The order with original expressions is 2.3, $\frac{5}{2}$, 4.

Arrange these rational numbers from largest to smallest: $\frac{4}{5}$, 0.9, $\frac{3}{6}$

Convert numbers: $\frac{4}{5}$ is 0.8, and $\frac{3}{6}$ is 0.5.

Understand the Relationship: Notice that $\frac{4}{5}$ is larger than $\frac{3}{6}$, but 0.9 is larger than both.

Order the Numbers: From largest to smallest, the order is 0.9, 0.8, 0.5.

Convert to Original Expressions: The order with original expressions is 0.9, $\frac{4}{5}$, $\frac{3}{6}$.

Ordering Rational Numbers on a Number Line

Rational numbers can often be close in value, which is why it is important to be accurate with your conversions of these numbers. Let’s look at the first problem from above, where the order from largest to smallest was 0.9, $\frac{4}{5}$, $\frac{3}{6}$. These values in decimal were 0.9, 0.8, 0.5. Let’s arrange these numbers on a number line.

Ordering Rational Numbers – Guided Practice

Let's practise ordering rational numbers together.

Arrange these numbers from largest to smallest: 0.6, $\frac{1}{5}$, 0.15

Ordering Rational Numbers – Application

Try solving these exercises on your own to practise ordering rational numbers!

Ordering Rational Numbers – Summary

Explore more with interactive exercises and quizzes on our platform. Keep practising, and you'll be a pro at ordering rational numbers in no time! If you're looking for more challenges, keep exploring our other resources including Sofahero!

Ordering Rational Numbers – Frequently Asked Questions