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# Numbers - Standard Form, Scientific and Engineering Notation

## The difference between standard, scientific and engineering number notation.

### Standard Form or Scientific Notation

A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is written in standard form or with scientific notation, ex.

43712 = 4.3712 104

0.036 = 3.6 10-2

### Engineering Notation

Engineering notation is similar to scientific notation except that the power of ten is always a multiple of 3, ex.

43712 = 43.712 103

= 0.043712 10

0.036 = 36 10-3

= 36000 10-6

Units used in engineering may be made smaller or larger with the use of prefixes, ex.

4.7 kJ = 4.7 103 J

= 4700 J

8 MV = 8 106 V

= 8000000 V

Prefixes used in the SI system.

Numbers written in scientific or engineering notation can be added or subtracted after they have been written with the same exponent. Example

4.3 104 + 2.4 103  =

4.3 104 + 0.24 104 =

(4.3 + 0.24) 104 =

4.54  104

#### Multiplication and Division

Numbers written in scientific or engineering notation can be multiplied or divided with the rules of exponential numbers.

#### Muliplication

N1 10x x N2 10y = (N1 x N2) 10x + y           (1)

##### Multiplcation Example

4.3 10 x 2.4 103  =

(4.3 x 2.4) 104+3 =

10.32  107

#### Division

N1 10x / N2 10y = (N1 / N2) 10x - y           (2)

##### Division Example

4.3 10 / 2.4 103  =

(4.3 / 2.4) 104-3 =

1.79  101

## Related Topics

• ### Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

• ### Decimal System Prefixes

Prefix names used for multiples and submultiples units.
• ### Designation of Large Numbers

Designation of large number in US vs. other countries.
• ### Exponents - Powers and Roots

The laws of fractional and integer exponents.
• ### Factorials

The product of all positive integers.
• ### Numbers - Square, Cube, Square Root and Cubic Root Calculator

Calculate square, cube, square root and cubic root. Values tabulated for numbers ranging 1 to 100.
• ### Roman Numerals

Roman numerals are a combinations of seven letters.
• ### SI System

An introduction to the SI metric system.
• ### Solving Equations of the First Degree with One Unknown

Equations with one unknown.
• ### Solving First Degree Equations with Two Unknowns

Online calculator and solbing procedure for two equations with two unknowns.
• ### Solving Quadratic Equation with One Unknown

How to solve a quadratic equation.

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## Citation

• The Engineering ToolBox (2011). Numbers - Standard Form, Scientific and Engineering Notation. [online] Available at: https://www.engineeringtoolbox.com/standard-form-scientific-engineering-notation-d_1801.html [Accessed Day Month Year].

Modify the access date according your visit.

7.25.9

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