| Category | Format | Size |
|---|---|---|
| Beijing Normal University eighth grade first volume mathematics | pptx | 6 MB |
"Understanding Irrational Numbers" Real Numbers PPT Courseware 2
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"Understanding Irrational Numbers" Real Numbers PPT Courseware 2
When a fraction is converted into a decimal, what are the final forms of the decimal?
Invite students to conduct activities in study groups: one student cites any fraction, and the other student converts this fraction into a decimal. And summarizes the form of this decimal?
Conclusion: Fractions can only be converted into finite decimals or infinite recurring decimals.
That is, any finite decimal or infinite recurring decimal is a rational number. Therefore, a and b are not rational numbers.
Numbers like 0.585885888588885…, 1.41421356…, -2.2360679… etc. have infinite decimal places, but they are not cyclic, but infinite non-cyclic decimals.
An infinite non-repeating decimal is called an irrational number. (Pi is also an infinite non-repeating decimal, so π is an irrational number)
True or False
(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. ( )
1. Irrational numbers are infinite decimals that do not repeat, and rational numbers are finite decimals or infinite recurring decimals.
2. Any rational number can be reduced to the form of fraction p/q (p≠0, p, q are integers and relatively prime), but irrational numbers cannot.
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.
What did you gain from this lesson?
1. The definition of irrational numbers.
2. How do you determine whether a number is irrational or rational?
3. How would you classify the numbers you have learned?
Let a circle with radius a have an area of 20π.
(1) Is a a rational number? Tell me your reasons.
(2) Estimate the value of a (accurate to tenths and use your calculator to verify your estimate).
(3) What if it is accurate to the percentile?
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For more information about the PPT courseware "Real Numbers Understanding Irrational Numbers", please click the Real Numbers ppt Understanding Irrational Numbers ppt tag.
"Understanding Irrational Numbers" Real Numbers PPT Courseware 3:
"Understanding Irrational Numbers" Real Numbers PPT Courseware 3 Learning Objectives 1. Understand the concept of irrational numbers and be able to determine whether a number is a rational number or an irrational number. 2. Be able to represent some simple irrational numbers on the number axis. In fact, any rational number can be written as a finite decimal Or infinite loop...
"Understanding Irrational Numbers" Real Number PPT Courseware:
"Understanding Irrational Numbers" Real Number PPT Courseware Think about it 1. Is the square of an integer always an integer? 2. Is the square of a fraction always a fraction? Recall that rational numbers include: integers and fractions. If a number is neither an integer nor a fraction, then the number is not...
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Update Time: 2024-06-30
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