Scientific notation is a method of counting.A number is expressed in the form of multiplying a by the n-th power of 10 (1 ≤ | a |<10, a is not a fractional form, and n is an integer)Numerationbe calledScientific notation.When we want to mark or operate a larger or smaller number with more digits, scientific notation saves a lot of space and time.[1]
Scientific notation is a method of counting.A number is expressed in the form of a multiplied by the n-th power of 10 (1 ≤ | a |<10, a is not a fractional form, and n is an integer). This notation is calledScientific notation.[2]For example: 19971400000000=1.99714 × 10 ^ 13.Calculators or computers usually use E or e to express the power of 10, that is, 1.99714E13=19971400000000.
Notation and benefits
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When we want to mark or operate on a larger or smaller number of digits, scientific notation saves a lot of space and time.[1]
form
The form of scientific notation consists of the product of two numbers.Expressed asa×10^b（aEb）
One of the factors isa(1 ≤ | a |<10), the other factor is10^n。
convenient
When using scientific notation to express numbers, the symbols of numbers are not changed, but the writing form of numbers is changed. It can conveniently express some large or small numbers encountered in daily life[3]。For example, the speed of light is about 300000000 m/s;The world population is about 8000000000[5].
This kind of number is inconvenient to read and write. We can avoid writing so many repeated zeros in the form of 6100000000=6.1 × 10 ^ 9,
Or: 0.00001=1 × 10 ^ - 5, that is, the number whose absolute value is less than 1 can also be expressed in the form of a times 10 to the negative nth power by scientific notation.
Notation
If | x |>1, it is recorded as
In the form of,
The value of is determined by
If m is the number of digits of x, then
,
If | x |<1, then
,
, where m is the digit of x, and m ₁ is the significant digit of x.
accuracy
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Using scientific notationa×10^nIts accuracy is based on the position of the last number of a in the original number.
For example:
13600, accurate to ten digits, recorded as: 1.360X10 ^ 4
13200, accurate to hundreds, recorded as: 1.32X10 ^ 4
322000, accurate to thousands, recorded as 3.22X10 ^ 5
operation
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Relevant expressions
aEb=a×10^b
（1）3×10^4+4×10^4=7×10^4
I.eaEc±bEc=﹙a±b﹚Ec
（2）3E6×6E5=18E11=1.8E12
I.eaEM×bEN=abE(M+N)
（3）-6E4÷3E3=-2E1
I.eaEM÷bEN=a/bE(M-N)⑷
Some related deductions
（aEc)^2=（aEc）（aEc)=a^2E2c
（aEc)^3=（aEc）（aEc）（aEc)=a^3E3c
（aEc）^n=a^nEnc
a×10^logb=ab
aElogb=ab
(1) N "E" formula 3E4E5=30000E5=3E9
That is, aEbEc=aEb+c
6E-3E-6E3=0.006E-6E3
=0.000000006E3
=6E-6
That is, aEbEcEd=aEb+c+d
Ea1Ea2Ea3....... Ean=aEa1+a2+a3++an
(2) N "E" formula and sequence
According to n "E" formula aEa1Ea2Ea3....... Ean=aEa1+a2+a3++an
Get aESn
The sum formula of equal difference n term na1+n (n-1)/2 × d
aEna1+n(n+1）/2×d
Equal ratio n term and formula Sn=a1n (q=1) an=a1 * q ^ n-1 (q!=0 n>=2 and q=1, an is a constant column) or n (1-q ^ n)/1-q
AESn [Sn=a1n (q=1) or n (1-q ^ n)/1-q (q ≠ 1)]
General term counting of series
Equivalence: aEan=aEa1+(n-1) d
Equal ratio: aEan=aEa1q ^ n-1
(3) AEb and aE-b
aEb=a×10^b
AE-b=a × 10 ^ - b plus or minus b determines the direction of E
Significance of scientific numeration
"AE" means that it is not of scientific numeration significance, and aE=a
"Ea" means scientific numeration meaning, that is, 1E3=1000 when Ea=1Ea a=3
stayMicrosoftExcelThe software canNumerical dataSet to scientific notation format. Take Excel 2010 as an example to introduce the setting method:
Step 1: Open the Excel 2010 worksheet window, and select the cell for which you want to set the scientific count format.Right click the selected cell, and select Set Cell Format from the shortcut menu.
Step 2: Switch to the Number tab in the Excel 2010 Format Cells dialog box that opens.Select the Scientific Count option in the Classification list, and set the number of decimal places in the Scale spinner on the right.Click OK after setting.[4]
