Scientific notation

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 10ⁿ

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 10²³

Example 2- Represent 1234.89 in scientific notation.

Representation in scientific notation is  1.23489 x 10³

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 10²  + 6.7532 x 10²

= ( 34.5765 + 6.7532) x 10²

= 41.3297 x 10²

= 41.33 x 10²

EX ) Add  3.65 x 10³ + 7.59 x 10⁴

= 0.365 x 10⁴ + 7.59 x 10⁴

= ( 0.365  + 7.59) x 10⁴

= 7.955 x 10⁴

= 7.96 x 10⁴

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 10³

= (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 10³

= (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 10⁶

= (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 10³/ 2.56 x 10⁵

= (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}

= (3.75 / 8.36)  x 10^{-3 -(-6)}

= 0.4485 x 10³

= 4.49 x 10²