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