Scientific Notation Calculations

To calm the nerves of those who deal with calculations, this invention is not less than a true blessing. Scientific notation is a precise way to express infinite numbers (small or large) in an understandable way.

The number is multiplied with ten by raising its power either positively or negatively. Positive power indicates large number while the negative power indicates small number.

Students that are studying mathematics, engineering, physics, chemistry usually deal with scientific notations. In this article, we will highlight how can we apply functions like addition, subtraction, division, and multiplication on standard form of numbers.

Area of Application

In Physics, scientific notation is used to represent velocity, displacement , distances, and to measure subatomic particles, etc.

In Chemistry, it is most vividly used to compute Avogadro’s number, molecular mass and weight.

Astronomers use it to measure the mass and distances of celestial objects.

How Scientific Notation Works

Mainly there are three different parts of scientific notation calculations. Exponent, base, and co efficient. For example 6.4*101 , in this example co efficient is 6.4, base is 10 , and exponent is 1.

There are certain rules to write a number in scientific notation.

Make sure that

Multiplication and Division of Scientific Notation

The rule for multiplying the numbers in scientific notation works in a way that coefficients are multiplied with the coefficients and later on powers are added. For example,


For division, you need to divide the coefficients and subtract the powers.

(a×10b)/ (c×10d)​=(a/c)×10 b-d

How to Add or Subtract Scientific Notation

There is one basic rule for applying addition or subtraction to the scientific notation. It is mandatory to align the exponents and then add or subtract the coefficients. Non alignment of the exponents will not effect the process but can make it a little bit difficult to simplify.

Adding 3.1×104 and 2.1×105, we can write it as 0.31×105 now both the terms have same exponents, multiply the coefficients 3.1×2.1 and add the exponents 4+5 to get the answer,

Same procedure will be applied when subtraction is done.


Scientific notation is an excellent way to arrange numbers in a way that they can be managed and computed accurately. Mastering its rules will make your journey towards mathematics and other subjects that involves calculations smoother.