# Scientific notation

Scientific notation is used to express very large numbers and very small numbers in standard form/ scientific-notation using exponents.

Scientific-notation is just a short hand way of expressing gigantic numbers like 615,000,000 or incredibly small numbers like 0.0000000000118. This method is used by engineers, mathematicians, scientists.
The study of exponents help us to express very large number such as 6,000,000,000 which is 6 x 10
9 and small numbers such as 0.000,000,006 as (6)/ 1,000,000,000 = 6 x 10 -9
• 1.2 ×10
14 -> the positive exponent indicates a large number.
• 7.89 × 10
-21 - > the negative exponent indicates a small number.
Note : The scientific numbers always lies between 0 and 10
( 0< number < 10)

 Scientific Notation Standard Form 4.23 ×102 423 4.23 × 103 4,230 4.23 ×104 42,300 4.23 ×105 423,000 4.23 ×106 4,230,000

Conversion of number into scientific- notation Write the following in scientific-notation :

1) 418500

As there is no decimal so consider the decimal after the number

= 418500
.
The decimal will shift 5 places to left, so the exponent of 10 is positive.
<
= 4.18 x 10
5

2) 26000000000

= 2.6 x 10
10 [ decimal will shift 10 places to left]

3) 0.0000056

As there is decimal

The decimal will shift 6 places to right, so the exponent of 10 is negative.
<
= 5.6 x 10
-6

4) 0.0000826

= 8.26 x 10
-5

5) 0.0000012 x 2500000000

Write each number in scientific-notation

0.0000012 = 1.2 x 10
-6

2500000000 = 2.5 x 10
9

So, 0.0000012 x 2500000000 =(1.2 x 10
-6 )x(2.5 x 10 9

= 3 x 10
-6+ 9

= 3 x 10
3

= 3000

Conversion of Scientific form to standard form Exponents

Laws of Exponents
Rational Exponents
Integral Exponents
Scientific notation
Solved examples on Scientific-Notation
Solved Examples on Exponents