What are Real Numbers? | Don't Memorise

TL;DR

Real numbers are any numbers that can be plotted on a number line, including positive and negative integers, non-terminating decimals, and irrational numbers.

Transcript

To understand what real numbers are, all you need to understand is the number line. Positive numbers to the right of Zero. And negative numbers to the left of Zero. You will hear various complicated definitions of real numbers but here's the simplest one. Any number, that can be plotted on a number line is called a real number. Let's look at a few ... Read More

Key Insights

• #️⃣ Real numbers can be represented on a number line.
• ❎ Real numbers include positive and negative integers, non-terminating decimals, and irrational numbers like pi and square root of 2.
• 🚱 Terminating decimals, non-terminating recurring decimals, and non-terminating non-recurring decimals are the three types of real numbers.
• #️⃣ Rational numbers and irrational numbers together form the category of real numbers.
• #️⃣ Rational numbers can be expressed as a fraction, while irrational numbers cannot.
• 🧡 Real numbers encompass a wide range of values and have various patterns of decimal representation.
• #️⃣ Understanding real numbers is essential in mathematics and their applications.

Questions & Answers

Q: What is the definition of a real number?

A real number is any number that can be plotted on a number line, including positive and negative integers, non-terminating decimals, and irrational numbers.

Q: Can non-integer numbers be considered real numbers?

Yes, non-integer numbers like decimals, including non-terminating decimals, can be plotted on a number line and are therefore considered real numbers.

Q: What is the difference between recurring and non-recurring decimals?

Recurring decimals are numbers that have a repeating pattern of digits after the decimal point, while non-recurring decimals do not have a specific pattern and continue indefinitely.

Q: How are rational numbers and irrational numbers related to real numbers?

Rational numbers, which include terminating and non-terminating recurring decimals, and irrational numbers form the category of real numbers. Rational numbers are numbers that can be expressed as a fraction, and irrational numbers cannot be expressed as a fraction and have non-recurring decimals.

Summary & Key Takeaways

• Real numbers can be plotted on a number line and include positive and negative integers, non-terminating decimals, and irrational numbers.

• Numbers with terminating decimal places, non-terminating recurring decimals, and non-terminating non-recurring decimals are the three types of real numbers.

• Rational numbers, which include terminating and non-terminating recurring decimals, and irrational numbers together form the category of real numbers.