"Real Numbers" PPT courseware 9

Description

"Real Numbers" PPT courseware 9

Induction: Any rational number can be written as a finite decimal or an infinite recurring decimal. (Characteristics of rational numbers)

Generalization: They are infinite non-repeating decimals, so we know they are neither integers nor fractions.

We call such infinite non-repeating decimals irrational numbers.

judge:

1. Real numbers are either rational or irrational. ( )

2. Irrational numbers are infinite non-repeating decimals. ( )

3. Irrational numbers are infinite decimals. ( )

4. Numbers with a root sign are irrational. ( )

5. Irrational numbers must always have a root sign. ( )

In the range of real numbers, the opposite numbers and absolute values ​​have exactly the same meaning as the opposite numbers and absolute values ​​in the range of rational numbers.

1. The opposite of a real number:

The opposite of a real number a is -a

(Just add a negative sign in front like the opposite of a rational number)

(2) Absolute value of real numbers:

1) The absolute value of a positive real number is itself;

2) The absolute value of a negative real number is the opposite of the negative real number;

3) The absolute value of 0 is 0 itself. The absolute value of a real number a is written as:

What did we learn in the last lesson?

real number(1)

1Irrational numbers: infinite non-repeating decimals

2 Common forms of irrational numbers:

(1) The square root can lead to endless numbers;

(2) Pi, π, and some numbers containing π;

(3) Regular but non-cyclic infinite decimals

4 Classification of real numbers: Dichotomy and Trichotomy.

5. The relationship between real numbers and the number axis: one-to-one correspondence

The main tasks of this lesson

1. Able to find the opposite and absolute value of a number in the range of real numbers.

2. Exploration of the properties of absolute values.

3. Operations on real numbers

Add, subtract, multiply, divide, exponent, square root

In the range of real numbers, the opposites, reciprocals, and absolute values ​​have exactly the same meaning as the opposites and absolute values ​​in the range of rational numbers.

The algebraic meaning of the opposite number:

Two numbers with different signs are called opposite numbers.

The geometric meaning of inverse numbers:

Two numbers represented by two points that are equidistant from the origin are opposite numbers to each other.

The geometric meaning of absolute value: the distance from a number to the origin

Through today’s study, talk about your gains and experiences in your own words?

1. Find the opposite and absolute value of a number (formula).

2. Absolute value properties: non-negativity (absolute value, square root of 2)

3. Arithmetic rules and properties of real numbers

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"Real Numbers" PPT courseware 11:

"Real Numbers" PPT Courseware 11 Review Questions Can you answer the following questions? (1) The opposite of 2 is ______, the opposite of - is ______, the opposite of 0 is ______; (2) |2& #124;=______, |-| =______, |0|=______. ... ... ..

"Real Numbers" PPT courseware 10:

"Real Numbers" PPT Courseware 10 Knowledge Review 1. Irrational numbers: infinite non-recurring decimals are called irrational numbers 2. Rational numbers: finite and infinite recurring decimals are rational numbers or integers and fractions are collectively called rational numbers. Think about (1) What have you known so far? number? ..

"Real Numbers" PPT courseware 8:

"Real Numbers" PPT Courseware 8 Integers and fractions are collectively called rational numbers. Finite decimals and infinitely recurring decimals are called rational numbers. Infinite non-recurring decimals are called irrational numbers. Induction 1. Every rational number can be represented by a point on the number axis; 2. Every irrational number ..

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Update Time: 2024-11-16

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