"Is square root 2 a rational number?" PPT courseware

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"Is square root 2 a rational number?" PPT courseware

Review & Thoughts

What are rational numbers?

rational numbers

integer

Positive integers: such as: 1, 2, 3,…

Zero: 0

Negative integers: such as -1, -2, -3,…

Fraction

Positive fractions: such as 1/2, 1/3, 5.2, …

Negative fractions such as -1/5, -5/6, -3.5, …

3.Are there any other numbers besides rational numbers?

Discuss

Can you try to find several such irrational numbers using various methods? Please explain the reason.

(1) The side lengths of squares with areas such as 5, 8, 10 and other non-square numbers;

(2) The height of an equilateral triangle with side length 2;

(3) By constructing a right triangle;

(4) Make a series of equations. For example, x²=3. etc.

emphasize

Like 0.585885888588885..., 1.41421356..., 2.2360679...0.101001000100001...the number of decimal places in these numbers is infinite, and they are not cyclic, they are infinite non-cyclic decimals.

Infinite non-repeating decimals are called irrational numbers.

(Pi=3.14159265... is also an infinite non-repeating decimal, so π is an irrational number, such as √2 mentioned above, etc. are all irrational numbers)

Any finite decimal or infinitely repeating decimal is a rational number.

Method points:

Determine whether a number is irrational:

(1) See if it is an infinite non-repeating decimal.

(2) All rational numbers can be written in fractional form, but irrational numbers cannot;

Specifically, it will be judged from the following aspects:

(1) Numbers with endless square roots are irrational numbers; (2) π is an irrational number; (3) infinite decimals that do not cycle (4) the sum and difference of irrational numbers and rational numbers must be irrational numbers; (5) irrational numbers and rational numbers (not The product and quotient of 0) must be irrational numbers;

Example 2 True or False Question

(1) Finite decimals are rational numbers; ( )

(2) Infinite decimals are all irrational numbers; ( )

(3) Irrational numbers are infinite decimals; ( )

(4) Rational numbers are finite decimals. ( )

Classroom presentation

1. Fill in the following numbers in the corresponding sets;

3.1415926 √7 0.6 -8 √33

2. Which of the following square side lengths is an irrational number ( )

A. A square with an area of ​​25;

B. A square with an area of ​​4/25;

C. A square with an area of ​​8;

D. A square with area 1.44.

3. The following statement:

(1) Rational numbers are all finite decimals

(2) Finite decimals are all rational numbers

(3) Irrational numbers are infinite decimals

(4) Infinite decimals are all irrational numbers.

The correct one is _______________.

4. A square with an area of ​​13cm2 has a side length of _______

5. It is known that the positive number m satisfies m2=39, then the integer part of m is ______

give it a try

As shown in the figure, it is made up of 16 small squares with a side length of 1. By arbitrarily connecting several vertices of these small squares, some line segments can be obtained.

(1) Each person must find at least 3 line segments with non-rational number lengths;

(2) Which is the longest non-rational number line segment?

Which is the shortest non-rational line segment? Why?

We don’t know the specific value of √2, so what is its size range?

By drawing, we find that the side length of a square with an area of ​​1 is 1, the side length of a square with an area of ​​4 is 2, and the side length of a square with an area of ​​2 is, that is, it is larger than 1 and smaller than 2, so its side length √2 should be between 1 and 2.

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"Is square root 2 a rational number?" PPT courseware 2:

"Is square root 2 a rational number?" PPT courseware 2 Learning objectives: 1. Understand and be able to give geometric explanations to irrational numbers 2, 3, 5, 7, 10, etc. 2. Be able to mark irrational numbers such as 2, 3, and 5 on the number line. Known: A line segment with unit length 1 (1) You can make a line segment with length 2..

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Update Time: 2024-10-01

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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