How to classify numbers | Numbers and operations | 8th grade | Khan Academy

TL;DR

This video explains the classification of numbers into rational, whole, and irrational categories.

Transcript

• [Voiceover] So we have a bunch of numbers listed up here, and my goal, in this video, is to see if we can classify them into different types of number categories, and let me draw the categories. So this circle, over here, this represents all of the numbers that can be represented as the fraction of two integers, and, of course, the denominator ca... Read More

Key Insights

• #️⃣ Numbers can be classified into rational, irrational, integer, and whole number categories.
• #️⃣ Rational numbers can be represented as the fraction of two integers.
• 🥳 Irrational numbers cannot be represented as the ratio of two integers.
• 🪡 Integers are a subset of rational numbers that do not need to be represented as a fraction or decimal.
• 🚱 Whole numbers are non-negative integers.
• 🔁 Numbers that repeat can always be represented as the fraction of two integers.
• ❎ The square root of a non-perfect square is always irrational.

Questions & Answers

Q: What is the difference between rational and irrational numbers?

Rational numbers can be represented as the fraction of two integers, while irrational numbers cannot.

Q: Are all whole numbers also integers?

Yes, all whole numbers are integers, but not all integers are whole numbers as integers can be negative as well.

Q: How can numbers that repeat be represented as a fraction?

Numbers that repeat can always be represented as a fraction of two integers. For example, 0.3 repeating is equal to one-third.

Q: Is the square root of a non-perfect square always irrational?

Yes, the square root of a non-perfect square is always irrational as it cannot be represented as the ratio of two integers.

Summary & Key Takeaways

• The video introduces the concept of rational and irrational numbers, with rational numbers being those that can be represented as the fraction of two integers, and irrational numbers being those that cannot.

• The categories of numbers are represented by circles, with the circle for rational numbers being larger than the circle for irrational numbers.

• Within rational numbers, there are integers (whole numbers) and a subset of integers known as whole numbers. The video explains the differences between these categories as well.