Scientific notation definition, what is scientific notation What is scientific notation

1. Definition and operation rules of scientific notation.

1. Definitions. Write a number in the form a 10na 10n (where 1 |a|<101≤|a|<10,n is a positive integer, and this form of counting is called scientific notation.

2. Calculation rules.

1) When the absolute value of the number to be represented.

When it is greater than 10.

Written in scientific notation as a 10na 10n, where 1 |a|<101≤|a|<10, n is a positive integer, and the value of n is equal to the number of digits of the integer part of the original number minus 1, as in 7453=.

2) When the absolute value of the number to be represented is less than 1.

Written in scientific notation as a 10na 10n, where 1 |a|<101≤|a|<10, n is a negative integer), and the value of n is equal to the inverse of all zeros that precede the first non-zero number in the original number.

Include the zero before the decimal point, such as .

3. Methods for determining aa and nn in the form of a 10na 10n in the form of scientific notation:

1) Move the decimal point to the end of the first digit from the left to get the value of AA;

2) There are two ways to determine nn.

One is to count the number of digits moved by the decimal point, and the decimal point moves by a few digits, and nn is how many;

The second is the integer number of digits of the original number, and the integer digits of the original number minus 1 is the value of nn.

2. Examples of scientific notation.

According to reports, Mr. Li, a resident of a community.

Improve water equipment and help him live in the community within 10 years.

of residents have saved 300 000 tons of water, and 300 000 is expressed in scientific counting.

It should be ( )a ㅤb. 3×1053×105 ㅤc. 3×1063×106 ㅤd. 30×10430×104

Answer: B Scientific notation.

Write a number in the form a 10na 10n (where 1 |a|<101≤|a|<10,n is a positive integer, and this form of counting is called scientific notation.

According to reports, Mr. Li, a resident of a certain community, improved water equipment and helped the residents of his residential community save a total of 300,000 tons of water in 10 years

Analysis: 300 000 = 3 105300 000 = 3 105So choose B

Scientific notation (also known in the UK as the scientific form or standard exponential form, or standard form) is a way of representing numbers that are too large or too small to be written in decimal system. It is commonly used by scientists, mathematicians, and engineers, in part because it simplifies certain arithmetic operations. On scientific calculators, it is often referred to as the "SCI" display mode.

In scientific notation, all the numbers are written in this form m 10 n

m multiplied by 10 to the nth power), where the exponent n is an integer and the coefficient m is an arbitrary real number. The integer n is called the order of magnitude, and the real number m is called the significant number or mantissa number. [1] However, the term "mantissa number" can be confusing because it is the name of the decimal part of a commonly used logarithmic.

If the number is negative, then the minus sign precedes m (as in ordinary decimal notation). In standard notation, an exponent is chosen so that the absolute value of the coefficient is at least 1, but less than 10.

Decimal floating-point is a computer arithmetic system that is closely related to scientific notation.

What is scientific notation.

1. Scientific notation refers to the form of expressing the companion width of a number book to the nth power of a 10, where 1 a<10, n is an integer.

2. The scientific notation method can easily represent some numbers with large absolute values, and similarly, the scientific counting method can also easily represent some chaotic absolute numbers with small absolute values. In general, a positive number less than 1 can be expressed as a 1o, where 1 a < 10 and n are negative integers.

Strictly speaking, multiplying 10 by 3 to the power is not scientific notation.

It should be multiplied by 10 to the power of 2.

When we want to mark or calculate a large or small one with a large number of digits, we use scientific notation to avoid wasting a lot of space and time.

The form of exact science notation is made up of the product of two numbers. Expressed as A10 B (AEB).

One of these factors is a(1 |a|<10), the other factor is 10 n.

When it is convenient to use scientific notation to represent numbers, the symbol of the number is not changed, but the writing form of the number is changed. It can easily represent some extremely large or small numbers encountered in daily life, such as: the speed of light is about 300,000,000 meters and seconds; The world's population is approximately:

Such a number is very inconvenient to read and write, we can avoid writing so many repeated zeros, and express it in the form of this: 6,100,000,000=, or:, that is, the number with an absolute value less than 1 can also be expressed by scientific notation as a times 10 to the negative n power.

1.Multiply by 10 to the power of 10.

2.The 20th power is an even power, so the defeat is 2 to the 20th power.

The 21st power is an odd power, so it is -2 to the 21st power.

Merge is -2 times 20 times without parentheses.

1.In scientific notation: 10000 = 1 10 4, 1000000 = 1 10 6 100000000 = 1 10 8

2.Please use scientific notation to represent the following numbers:

1) The radius of Mercury is 2440000 meters = meters (2) Jupiter's equatorial radius is about 71400000 meters = meters (3) The land area of the Earth is about 149000000 km 2 = km (4) The area of the oceans on the Earth is about 361000000 km 2=km 23What are the following numbers expressed in scientific notation?

1) The area of the Forbidden City in Beijing is about 2 = 720,000 meters 2 (2) There is about one red blood cell in the human body.

3) Globally, about m3 of water is converted from the oceans and land into water vapor in the atmosphere every year m3=57700000000000000m3

You're so stupid, you can't do it that simple.

The notation of an integer with an absolute value greater than 10 (or less than 1) as a 10 n (where 1 manuscript is called a <10) is called scientific notation. For example, quietly dismantling 5000 = 5x10 3

Input: Data expressed in scientific notation. That is, it is a scientific notation representation that conforms to the C language representation.

Output: A double-precision representation of the data.

Instructions: 1The accuracy of the input data is not higher than 50 decimal places.

2.When entering data, there is a space between the real number and the power to separate it, and the number of spaces is indefinite.

3.The result is kept to 8 decimal places, if it is less than 8 digits, it is made up with 0, and if it exceeds 8 digits, it will be truncated and not rounded.

Programming ideas:1The input data is read one by one in the form of characters, the mantissa part is stored in a string, and the exponential part is converted to an integer for saving. Do not save the mantissa part as a real number, because the decimal part of the mantissa may be large, and the accuracy of saving it with a real number is not enough.

2.Check if there is a decimal point in the mantissa string, and if the mantissa entered does not have a decimal point, insert a decimal point in the string.

3.Move the decimal point based on a given exponential value, there may be the following:

1) The exponent is positive, and the decimal is shifted to the right.

38 divided by 1000000*13*10 to the power of 8 = -5 to the power * 13 * 10 to the power of 8.

to the power of (-5+8).

to the 3rd power. to the 4th power.