# Numbers - Standard Form, Scientific and Engineering 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 10 ^{4 }*

* 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 10 ^{3} *

* = 0.043712 10 ^{6 } *

* 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 10 ^{3} J *

* = 4700 J *

*8 MV = 8 10 ^{6} V *

* = 8000000 V*

Prefixes used in the SI system.

#### Addition and Subtraction

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

*4.3 10 ^{4 }+ 2.4 10^{3} =*

*4.3 10 ^{4 }+ 0.24 10^{4} =*

*(4.3 + 0.24) 10 ^{4} =*

*4.54 10 ^{4}^{ }*

#### Multiplication and Division

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

#### Muliplication

*N _{1} 10^{x} x N_{2} 10^{y} = (N_{1} x N_{2}) 10^{x + y} (1)*

##### Multiplcation Example

*4.3 10 ^{4 } x 2.4 10^{3} =*

*(4.3 x 2.4) 10 ^{4+3 }=*

*10.32 10 ^{7}*

#### Division

*N _{1} 10^{x} / N_{2} 10^{y} = (N_{1} / N_{2}) 10^{x - y} (2)*

##### Division Example

*4.3 10 ^{4 } / 2.4 10^{3} =*

*(4.3 / 2.4) 10 ^{4-3 }=*

*1.79 10 ^{1}^{ }*

## Related Topics

### • Mathematics

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

## Related Documents

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### Designation of Large Numbers

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### Exponents - Powers and Roots

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### Solving Equations of the First Degree with One Unknown

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### Solving Quadratic Equation with One Unknown

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