Scientific notation-

## Scientific notation-

* A better and simplified way to represent very large or very small values is called scientific notation. It is also called exponential notation.*

Scientific notation is a way to represent very large & very small numbers between 1.000 and 9.999 by dividing or multiplying by 10 to an appropriate number of times.

**The very large or small number is expressed in terms of scientific notation like N x 10^{n}**

Where * N is number* and

**n is the exponent.****Example 1 – Avodagro’s number is 602,213,700,000,000,000,000,000. It is written in scientific notation like 6.022 x ***10*^{23}

*10*

^{23}**Example 2- Represent 1234.89 in scientific notation.**

**Representation in scientific notation is **1.23489 x *10*^{3}

^{3}

*While performing mathematical operations on numbers expressed in scientific notation the following points are to be remembered.*

## Addition & Subtraction-

*During addition and subtraction, exponent ( power of 10 ) must be the same.*

**EX ) Add 3457.65 + 675.32**

= 34.5765 x *10 ^{2}* + 6.7532 x

*10*

^{2 }= ( 34.5765 + 6.7532) ** x 10^{2}**

**= 41.3297 x 10^{2}**

**= 41.33 x 10^{2}**

### EX ) Add 3.65 x *10*^{3} + 7.59 x *10*^{4}

^{3}

^{4}

= 0.365 x *10 ^{4}* + 7.59 x

*10*

^{4}= ( 0.365 + 7.59) x *10 ^{4}*

= 7.955 x *10 ^{4}*

**= 7.96 x 10^{4}**

## Multiplication –

*In multiplication ,follow the relation (10 ^{x} ) x (10^{y}) =10 ^{x + y}*

### Ex 1) Multiply 2.14 x *10*^{-5} x 3.56 x *10*^{3}

^{-5}

^{3}

= (2.14 x 3.56 ) x *1o ^{3 – 5}*

= 7.6184 x *10 ^{3 – 5 }*

**= 7.62 x 10 ^{-2}**

### Ex 2) Multiply 3.24 x *10 *^{2} x 2.76 x *10*^{3}

^{2}

^{3}

= (3.24 x 2.76) x 10 * ^{2+3}*

= 8.9424 x *10 ^{ 2+ 3 }*

**= 8.94 x ****10 **^{5 }

### Ex 3) Multiply 4.26 x *10 *^{5} x 8.47 x *10*^{6}

^{5}

^{6}

= (4.26 x 8.47) x *10 ^{5 + 6}*

= 36.0822 x *10 ^{5+ 6 }*

= 36.0822 x *10 ^{11}*

**= 3.61 x 10 ^{12}**

## Division –

In division follow the relation (*10 ^{x}* ) / (

*10*

^{y}*) =10*

^{x – y}### EX 1) Divide 6.75 x *10*^{3}/ 2.56 x *10*^{5}

^{3}

^{5}

= (6.75 / 2.56) x *10 ^{3 – 5
}*

**= 2.64 x 10^{ -2}**

### EX 2) Divide 3.75 x *10*^{– 3}/ 8.36 x *10*^{– 6}

^{– 3}

^{– 6}

= (3.75 / 8.36) x *10 ^{-3 -(-6)}*

= 0.4485 x *10 ^{3}*

**= 4.49 x 10^{2}**