Scientific Notaion

Scientific notation is a way of expressing very large or small numbers in a contracted form. Numbers like 1500000000 or 0.0000000061 are inconvenient to use. The first number is quite lager to memorize while second number is  quite small to memorize. They can be made convenient to use by writing them in scientific notation as;

1.5 x 10^9
6.1 x 10^-9

Let's learn the art of writing large or small measurements in scientific notation

Parts of scientific notation

Scientific notation has three parts. You can see them in the given figure.

Value of coefficient is equal to or greater than it but its value cannot be increased after 10.
Base is always 10.
Exponent is the power of base i.e. 10 which can raise it according to its quantity.

Tips to remember while writing measurement in scientific notation

Tip #1. If the given measurement is greater than one, the power of ten is positive.

Tip #2. If the given measurement is small than one, the power of ten is negative.

 How to write the numbers in scientific notation

Example 1:- The distance from earth to  sun is 150,000,000 km away from sun. Express  it in scientific notation.

Solution

Here coefficient is 1.5

Power of ten is 8.

As the number is greater than one,
the exponential term is positive here.

1.5 x 10⁸ km

Example 2 :- Size of an typical bacteria is 0.0000064 m. Express the notation in standard form (scientific notation).

Here coefficient is 6.4

Power of 10 is  -6

Exponential power is negative because the given notation is smaller than one.

6.4 x 10^-6 m