"Approximate Numbers" PPT courseware

"Approximate Numbers" PPT courseware

learning target:

Understand the concept of approximate numbers.

Able to obtain approximate numbers as required, and be able to point out the precise digits of the approximate numbers.

Understand the application of approximate numbers in real life.

Let students feel that mathematics comes from life and serves life.

How are these numbers expressed?

√2=1.41421356237309504880……….

π=3.1415926535897932384626………..

1. Collect data and understand life:

The number of students in my class, the number of boys and the number of girls;

The length and width of your desk;

number of pages in a mathematics textbook;

Your weight, your height;

China's population.

Among these data, which numbers are consistent with reality? Are those numbers close to reality? Can you find some more data from the life around you?

Accurate number - a number that exactly corresponds to reality

Approximate number - a number that is very close to the actual number

2. Use the rounding method to determine the value of pi =3.1415926 as required:

(1)π≈____ (retain integers)

(2)π≈____ (retain 1 decimal place)

(3)π≈______ (retain 2 decimal places)

(4)π≈______ (retain 3 decimal places)

Precision - indicates how close an approximate number is to the exact number

Example 1: Which of the following approximate numbers obtained by rounding is accurate?

1) 5.67 2) 43

3) 43.0 4) 2.04

5) 20,400 6) 1.212 billion

7) 1.11×104 8) 3.0×103

Do the approximate numbers 43 and 43.0 represent the same accuracy?

Do the approximate numbers 2.04 and 20,400 represent the same accuracy?

Example 2: Use the rounding method to approximate the following numbers according to the requirements in brackets.

(1) 0.0158 (accurate to thousandths)

(2) 304.35 (accurate to single digit)

(3) 1.804 (accurate to 0.01)

(4) 125.5991 (accurate to 0.01)

(5) 2056 (accurate to thousands)

(6) 2056 (accurate to hundreds)

(7) 34567 (accurate to thousands)

(8) 1087321 (accurate to 10,000 digits)

Exchange and discussion

In a physical examination organized by the school, two classmates, Xiaobei and Xiaochen, both measured about 1.7 meters in height, but Xiaobei said that he was 9 centimeters taller than Xiaochen. Do you think this is possible?

Please explain why.

The range of the exact number X represented by the approximate number 1.7 ( )

A 1.65 ≤ X < 1.75 B 1.69 ≤ X ≤ 1.74

C 1.70 ≤ X < 1.75 D 1.65 ≤ X ≤ 1.75

Connect with reality and enter life

1. The length, width and height of a disposable chopstick are approximately 0.5cm, 0.4cm and 20cm. It is estimated how much wood is used to make 10,000 pairs of disposable chopsticks and how many trees need to be cut down. The radius is 0.1m and the height is 10m (excluding unusable treetops) ) to obtain this wood? (results are kept as integers)

Class summary:

1. Approximate numbers.

1. Use the rounding method to approximate the logarithm according to the requirements in parentheses.

2. Some points to note:

1. The two approximate numbers 1.8 and 1.80 represent different degrees of accuracy.

2. The two approximate numbers 20,400 and 2.04 have different precise digits.

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