Scientific Notation:
In scientific notation, we write numbers as \(x \times 10^{y}\), where \(x \geq1\) and \(x<10\) is the coefficient and \(y\), is the exponent,is any integer.
Example:
1.\(3430000 = 3.43 \times 10^{6}\)
2. \(0.0059 = 5.9 \times 10^{-3}\)
Linear Vs Exponential Growth:
Linear Growth: Repeated addition of constant value
Exponential Growth: Repeated multiplication of constant value
Example:
To cover the distance between Earth and Moon
With linear growth it takes \(1,92,20,00,000\) steps with each step is \(20 \ cm\) gain.
With exponential growth it takes \(46\) folds of a piece of paper.
Very Large Numbers & Order of Magnitude:
Scientific notation is used to express larger quantities.
Example:
Stars in Universe: \(2 \times 10^{23}\)
Ant population: \(2 \times 10^{16}\)