# Compare Rational Numbers by Scientific Notations

Rational numbers are terminating or recurring decimal numbers written in the form of fraction $\frac{a}{b}$ in which 'a' and 'b' are integers and the denominator 'b' not equal to zero. Rational numbers can also be represented using Scientific Notations. Scientific Notations is the shorthand way of writing numbers. Power of 10(exponents) is used to represent the number.

e.g, 12.256 is a Rational Numbers and can be represented in Scientific Notations as 0.1226 * 102.

It is easy to compare rational numbers when its represented using scientific notation. To compare a number available in scientific notation first, we have to compare power of 10 and then we compare Decimals.

Example: Compare the following numbers 0.065 * 108, 112 * 102, 0.45 * 107

1. Write the rational numbers in scientific notations.

6.5 * 106, 1.12 * 104, 4.5 * 106

2. Order them according to the power of 10. If its is same then order the decimal values.

1.12*104, 4.5*106, 6.5*106

3. Write all the rational numbers in their original form.

112*102, 0.45*107, 0.065*108