"Division of Powers with the Same Base" Multiplication and Division of Integers PPT (Lesson 2)

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"Division of Powers with the Same Base" Multiplication and Division of Integers PPT (Lesson 2)

Part One: Learning Objectives

Be able to express positive numbers less than 1 in scientific notation, perform their multiplication and division operations, and express the results in scientific notation.

review review

We know that nanometer is a unit of length, 1 meter = 1 000 000 000 nanometers, expressed in scientific notation: 1 meter = 1 × 109 nanometers; conversely,

1 nanometer = ______ meter? Can this result still be expressed in scientific notation?

Division of powers with the same base PPT, Part 2: Problem Situation

Yao Tandong, academician of the Chinese Academy of Sciences and member of the Chinese People's Political Consultative Conference, recited a few lines from "Qinyuan Spring Haze" in front of General Secretary Xi, which was ridiculed by everyone, "Beijing scenery, thousands of miles of haze, thousands of miles of dust... The air is so bad that it attracts countless beauties to wear Mask." There was a burst of laughter at the scene. At the same time, it also shows that people across the country are paying attention to PM2.5. How much do you know about PM2.5?

PM2.5 refers to particulate matter in the atmosphere with a diameter less than or equal to 2.5 μm, also known as particulate matter that can enter the lungs. Its diameter is less than 1/20 the thickness of a human hair. PM2.5 has a small particle size and is rich in toxic and harmful substances. It stays in the atmosphere for a long time and is transported over long distances. It is known as the culprit of air pollution.

Assume that the diameter of a particle that can enter the lungs is about 2.5 μm, which is equivalent to how many meters? How many such particles connected end to end can reach one meter?

2.5÷1000000=0.0000025(m)

Such a result is too small and inconvenient to express. Can we use scientific notation to express a number whose absolute value is less than 1?

Division of powers with the same base PPT, part three: exploring new knowledge

Let’s first calculate the following problem:

In turn, 0.000001=10-6, 0.000000001=1×10-9. It can be seen that a number with an absolute value less than 1 can be expressed by a negative exponential power of 10.

0.0000000051=5.1×10-9;

0.0000301=3.01×10-5.

Generally: we write numbers with absolute values ​​less than 1 in the form a×10n (n is a negative integer, 1≤a<10).

What is the difference and connection between it and the previously learned number whose absolute value is greater than 1, expressed in scientific notation as a×10n (n is a positive integer)?

If the absolute value of a is greater than 1, n is a positive integer; if the absolute value of a is less than 1, n is a negative integer.

Division of powers with the same base PPT, Part 4: Typical examples

example 1. Assume that the diameter of a particle that can enter the lungs is about 2.5 μm, which is equivalent to how many meters? How many such particles connected end to end can reach 1m?

Solution: Original method:

2.5μm=0.0000025m, 1÷0.0000025=400000 (pieces)

Current method:

2.5μm=2.5×10-6m, 1÷(2.5×10-6)=4×105 (pieces).

Example 2． (1) China Business Network reported on June 18, 2014 that a robot weighing 0.000106 kg, with a body made of carbon fiber and only the size of an insect is the world's smallest robot. 0.000106 can be expressed in scientific notation as ( )

A. 1.06×10-4 B. 1.06×10-5

C． 10.6×10-5 D. 106×10-6

(2) The following numbers are expressed in scientific notation ( )

A.-2×10-2 B.0.12×103 C.12.3×10-4 D.541×10-2

(3) The result of expressing 0.0000432 in scientific notation is ( )

A.4.32×10-4 B.4.32×10-5 C.0.432×10-5 D.0.432×10-6

Example 3. The mass of the sun is about 1.2×1027 tons, and the mass of the earth is about 6×1024 kilograms. How many times the mass of the sun is the mass of the earth?

Solution: 1.2×1027 tons = 1.2×1030 kilograms,

(1.2×1030)÷(6×1024)=2×105

The mass of the sun is 200,000 times the mass of the earth.

Division of powers with the same base PPT, Part 5: Practice in class

1. (1) Using scientific notation to record the coal reserves on the earth, the number estimated to be 15 trillion tons is ()

A. 1.5×1012B. 0.15×10 15 C. 15×1012 D． 1.5×10 13

(2) There are 2,000 teachers and students in a school. If each person borrows 10 books, then the National Library of China has a total of 200 million books. How many such schools can be borrowed (　)

A. 1000B． 10000C． 100000 D． 2000

(3) my country’s oil production in a certain year is approximately 170,000,000 tons, expressed in scientific notation as ()

A. 1.7×10-7 　B． 1.7×107 C． 1.7×108　D． 1.7×109

2. Use the scientific sum method to express the following numbers: -362000=_______________;

0.0000192=_______________; 173.9=_______________.

-0.000003875=___________ (retain three significant digits)

Division of powers with the same base PPT, Part 6 content: Class summary

Use scientific notation to represent a number with an absolute value less than 1:

Generally, a positive number less than 1 can be expressed as a×10n, where 1≤a<10 and n is a negative integer.

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"Division of Powers with the Same Base" PPT download of multiplication and division of integers:

"Division of powers with the same base" PPT download of multiplication and division of integers Part 1: Objectives of this section 1. Explore the operation process of division of powers with the same base, and develop cooperative communication skills, reasoning skills and organized expression skills. 2. Correctly apply the algorithm of division of powers with the same base.

"Division of powers with the same base" PPT on multiplication and division of integers (Lesson 1):

"Division of Powers with the Same Base" Multiplication and Division of Integers PPT (Lesson 1) Part One Content: Learning Objectives 1. The algorithm of division of powers with the same base and its application; 2. The process of exploring the algorithm of division of powers with the same base, Able to perform division operations of powers with the same base; 3. Palm...

"Division of Powers with the Same Base" PPT download:

"Division of powers with the same base" PPT download Part 1 content: Knowledge review 1. Division of powers with the same base, base ____, exponent ___. 2. aman=____ (a0, m, n are all positive integers, and mn) 3 .Calculation: (1) 279973 (2) b2mbm-1 (m is an integer greater than 1)..

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Update Time: 2024-09-15

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