In a number line the number increases going from left side to right side. If we move to the right side we are moving in the positive direction. If we move to the left side we are moving in the negative direction. In a number line any number to the left of another number is considered to be smaller than the number to its right. One can order the numbers by arranging them from smallest to the largest or the largest to the smallest.

To find the largest or smallest number in a set of numbers one has to compare each number with one another. In this section we will be learning more about how to compare numbers and the symbols used for that.

## How to Compare Numbers

The following are the symbols and terms used for comparing numbers.
The symbol for greater than $(>)$, less than $(<)$ and equal to $(=)$ are used to compare numbers:

a) Greater than $(>)$: It means that the first number is larger than the second number.

b) Less than $(<)$: It means that the first number is smaller than the second number.

c) Equal to $(=)$: It means that both the numbers have the same value.
Examples:
1) 123 > 100, 123 is greater than 100

2) 450 > 325, 450 is greater than 325

3) 229 < 864, 229 is less than 864

4) 512 < 1221, 512 is less than 1221

5) 15 = 15 , 15 is equal to 15

## Comparing Numbers in Scientific Notation

Scientific notation is a different way to write numbers, it is an extremely useful and convenient way of writing very small and very large numbers. The number 600 is the same as $6 \times 100$ which is the same as $6 \times 10^{2}$.

Scientific Notation must have a number between 1 and 10 multiplied by a power of 10.

To compare the number in scientific notation:

a) If the powers of the $10$ are the same, compare the first factors of each number.

b) If the powers of the $10$ are different, compare the exponents of each number.
In order to compare number written in scientific notation, one could write each number out in standard form. And to decide which is larger, begin by looking at the power of $10$. Remember that the positive powers of $10$ represent large number and the negative powers of $10$ represent small number. And if one want to compare a number having same powers of $10$. one must look at the first numbers.

Example 1: When comparing $5.7 \times 10^{6}$ and $10.2 \times 10^{-4}$ one can see that

$5.7 \times 10^{6}$ > $10.2 \times 10^{-4}$

Example 2: Compare $3.25 \times 10^{5}$ and $6.35 \times 10^{5}$

Since the powers of $10$ is same we have to look at the first number, that is $6.35 > 3.25$

Hence we can write $6.35 \times 10^{5}$ > $3.25 \times 10^{5}$

Example 3: Which is larger $5.25 \times 10^{-5}$ or $7.25 \times 10^{-3}$

Solution: To compare the numbers in scientific notation, first compare the powers of $10$.

Since $-3 > -5$, then $7.25 \times 10^{-3}$ > $5.25 \times 10^{-5}$.