"Why Are Numbers Not Enough Again?" Real Number PPT Courseware

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"Why Are Numbers Not Enough Again?" Real Number PPT Courseware

1. Think about it

1. How are rational numbers classified?

Rational numbers and integers (such as -1, 0, 2, 3,...): can be regarded as finite decimals.

Fractions (such as -3/2, 2/5, 9/11...): Can they all be converted into finite decimals or infinitely recurring decimals?

2. In the last class, we learned that some numbers, such as a2=2 and b2=5, are neither integers nor fractions. So what exactly are they?

Conclusion: a and b are neither integers nor fractions, then a and b must not be rational numbers.

When a fraction is converted into a decimal, what are the final forms of the decimal?

Invite students to conduct study group activities: 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.

Numbers like 0.585885888588885…, 1.41421356…, 2.2360679… etc. have infinite decimal places, but they are not cyclic, they are infinite non-cyclic decimals.

Therefore, an infinite non-repeating decimal is called an irrational number. (Pi=3.14159265... 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. ( )

emphasize

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, q are integers and relatively prime), but irrational numbers cannot.

Inquiries and Activities:

The radius of a circle with a design area of ​​5π is a.

(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?

Who was the first to use the symbol π to represent pi?

The irrational number π represents pi. When did π begin to be used to represent pi? Why use the letter π?

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"Why Are Numbers Not Enough Again?" Real Number PPT Courseware 2:

"Why Are Numbers Not Enough Again?" Real Number PPT Courseware 2. Can you help? a. Xiaohong is a freshman who has just entered eighth grade. One weekend morning, her father, who is an engineer, asked Xiaohong two math problems: (1) Are the two numbers 3.252525 and 3.252252225 the same? it..

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Update Time: 2024-11-22

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