Scientific Notation

In science, we measure, calculate, round off numbers,  We encounter very small and large numbers which need to be calculated.  You will encounter problems if you do not know what is a scientific notation because even calculators when dealing with big and very small numbers convert the answers to scientific notation.  This post will help you how to write numbers in scientific notation and vice versa.


What is Scientific Notation?

Scientific notation is a shorter way of writing very large and small numbers.  It has a general form of

N x 10ⁿ 

where

               N  is a number which is not less than 1 and not more than 10

               n  is an exponent, it can be positive or negative integer (whole number)

Let us see for example we have 1 g of hydrogen, it contains this number of atoms

602,200,000,000,000,000,000,000

How to write number, in scientific notation form?

In expressing number in scientific notation, we have to locate the decimal point.  In a large number like the example above it shows no decimal point but it is fully understood that the decimal point is located at the last zero.  Now in setting the N we have to move the decimal point such that we can get a number that is in between 1 and 10.  And so we should move the decimal point to the left stopping in between 6 and 0, the number should be 6.02, then copy x 10.

Now in determining the value of n, we need to count the number of decimal places the point has moved.  From the last zero to in between 6 and zero it takes 23 decimal places and moving to the left and so the final scientific notation of the number above is

6.02  x  10²³

The exponent is positive since we moved the decimal point to the left which indicates that the number is a big number.

Let us have another example, the mass of 1 hydrogen atom which is

0.000 000 000 000 000 000 000 001 66 g

In this example, we set the value of N by moving the decimal point to  in between 1 and 6 to have 1.66 as the value of N.  To determine the exponent, we count the number of decimal places the point has moved.   It takes 24 decimal places from left to right which means that the exponent is negative that indicates that the number is very small number. Below is the scientific notation form of the number above:

1.66 x 10^-24 g 

In summary, we can write very small and large number in  scientific notation in two ways:

1.  Just set the value of N by moving the decimal point such that you can have a number in between 1 and 10.

2.  In determining the value of n, or the exponent, we just count the number of decimal places the point has moved.  The number of decimal places is the exponent.   Once the decimal point is moved from right to left, the exponent is positive and when move from left to right the exponent is negative.

More examples:

Write the scientific notation of the following numbers:

a.  0.000 000 005 5  

b.  0.000 000 000 000 430

c.   2,000,000

d.   400,000 000 000

Solution:

a.  5.5 x 10^-9

b.  4.30 x 10^-13

c.  2.0 x 10⁶

d. 4.0 x 10¹¹

How to convert  scientific notation to ordinary number?

Here are simple ways to convert scientific notation to ordinary number:
1.  Identify if small number or big number by looking at the exponent.  If the exponent is positive; it means its a big number if negative; its a small number.  Once positive we need to add zeros to the right and once negative we will add zeros to the left.

2.  Add zeros by also counting the decimal places equivalent to the exponent starting from the decimal place where the decimal point is located.

Example:

1.  3.55 x 10⁶  

     The exponent is a positive integer, meaning it's a big number; therefore we need to add zeros to the right.  It doesn't mean you will add 6 zeros but you have to count starting from the decimal place in between 3 and 5 where the decimal point is located.  Moving to the right adding zeros until you reach 6 decimal places.  And so the answer is 3,550,000.

2.  6.23 x 10^-9

      The exponent above is negative integer, which means the number is very small number; and so we need to add zeros to the left. In adding zeros you need to count the number of decimal places the decimal point is moved following the exponent.  The answer for number two example is
0.000 000 006 23.

 I hope you learn something from this post. Just try below:


TRY THIS:

1.  Write the numbers below in scientific notation:
     a.  345,000,000,000
     b.  5,000,000,000,000,000
     c.  0.000 000 000 000 000 000 4
     d.  0 000 567
     e.  0.000 000 008 5


2.  Convert the scientific notation below to ordinary number
     a.  8.5 x 10^-7
     b.  1.23 x 10^-12
     c.  4.30 x 10⁵
     d.  3.33 x 10⁹
     e.  2.9 x 10^-15

For addition, subtraction, multiplication and division of scientific notation click HERE.