What are Real Numbers?; Rational vs. Irrational Numbers; Understanding Number Types; Ordering Real Numbers; Real Numbers in Everyday Life

Exploring Real Numbers

Mathematics

Exploring Real Numbers

Discover the numbers that make up our world!

Agenda

• What are Real Numbers?

• Rational vs. Irrational Numbers

• Understanding Number Types

• Ordering Real Numbers

• Real Numbers in Everyday Life

What Are Numbers?

Numbers are all around us, from checking the temperature to scoring points in a game. We use them for so many things every day. What different kinds of numbers do you think exist?

Numbers in everyday life: homes, toys, clothing, and objects.

Introducing Real Numbers

Real numbers are all the numbers you can find on a number line. This includes numbers you already know, like 5, -3, or 1/2. We'll also explore some new types of numbers that fit here too.

Natural numbers on a number line: understanding real numbers.

Numbers You Already Know

• Natural Numbers: Counting numbers (1, 2, 3, ...), like 5 friends.

• Whole Numbers: Natural numbers plus zero (0, 1, 2, ...), like 0 points.

• Integers: Whole numbers and their negatives (...-2, -1, 0, 1, 2...), like -10 degrees.

What Are Rational Numbers?

Rational numbers are any numbers that can be written as a fraction, like a/b. Here, 'a' and 'b' must be whole numbers (integers), and 'b' cannot be zero. For example, 3/4, -5 (which is -5/1), and 0.75 (which is 3/4) are all rational numbers.

Natural numbers on a number line: a visual aid.

Rational Decimals

Rational numbers can be written as decimals that either stop (terminate) or repeat a pattern endlessly. For instance, 1/2 is 0.5 (terminating), and 1/6 is 0.1666... (repeating). These predictable decimal forms are key characteristics of rational numbers.

1/3 as a repeating decimal: 0.33...

Are These Rational?

• 7

• 1/3

• 0.25

• √2

What Are Irrational Numbers?

Unlike rational numbers, irrational numbers have decimals that never end and never repeat. This means they can't be expressed as a simple fraction of two integers. Famous examples include Pi (π) and the square root of 2 (√2).

Irrational numbers: non-repeating, non-terminating decimals like π and √2.

Famous Irrational Numbers

Some irrational numbers are very famous! Pi (π) is about 3.14159... and helps us find the circumference and area of circles. The square root of 2 (√2), approximately 1.414..., is important in geometry, like finding the diagonal of a square.

Pi (π) helps calculate circle circumference: C = 2πr.

Visualizing square roots with colored cubes, like the square root of 2.

Exploring Real Numbers

What are Real Numbers?; Rational vs. Irrational Numbers; Understanding Number Types; Ordering Real Numbers; Real Numbers in Everyday Life

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