In this page , we are going to discuss about Exponents and Scientific Notation.
Exponent of a number shows you how many times the number is to be used in a multiplication.
For example 2 x 2 x 2 x 2 x 2 can be written as 2⁵, we read it as “Two raised to the power 5” or fifth power of two, or we can say simply 2 to the power five. Here 2 is called the base and 5 is called the index or exponent.
Here are laws:
In Exponents and Scientific Notation, scientific-notation is one of the ways of writing numbers that are too large or too small to be conveniently written in decimal representation.
In subjects, such as astronomy, physics, chemistry and engineering, we come across very large numbers and very small number. For example if we have,
(i) The distance of earth from sun is about 92,900,000 miles.
(ii) The average cell is containing about 200,000,000,000 molecules.
Such numbers are not so easy and manipulate in the decimal form. However, they can be written and manipulated easily using the laws of indices. If "m" is natural number and a is a real number, then aᵐ means the product of m numbers each equal to a, that is, aᵐ= a x a x a ………..m factors. Here a is known as base and m, the power or exponent or index.
When the number is written in scientific notation a x 10ⁿ, the integral part of the number, a is a digit from 1 to 9 and the power of 10 is an integer (positive , negative or zero). We also observe that while converting a given number into scientific notation, if the decimal point is moved r places to the left, then this movement is compensated by factor 10 ʳ, and if the decimal point is moved r places to the right, then this movement is equated by the factor 10
Here are some examples, Exponents and Scientific Notation
Uses of scientific notation:
When very large or very small numbers are put in the scientific notation, that can be multiplied or divided easily using this form.
Here are more examples:
Write the following numbers in scientific notation:
(1) 7493 = 7.493 x 10 ³
(2) 105001 = 1.05001 x 10 ⁵
(3) 3449099.93 = 3.44909993 x 10 ⁶
(4) 0.00567 = 5.67 x 10 ⁻³
(5) 0.0002079 = 2.079 x 10⁻⁴
Write the following numbers in decimal form:
(1) 3.25 x 10 ⁵ = 325000
(2) 1.86 x 10⁷ = 18600000
(3) 9.87 x 10 ⁹ = 9870000000
(4) 4.02 x 10⁻⁴ = 0.000402
(5) 1.423 x 10⁻⁶ = 0.000001423