Scientific notation

Scientific notation, or exponential notation as it is also known, is a handy way to manage extremely large numbers such as the Earth's mass and miniscule values such as the mass of a hydrogen atom. These types of numbers are not easily manageable when one is required to insert all the zeros. When we use exponents with 10 as a base, we have:

$10^{1}=10$

$10^{2}=100$

$10^{3}=1000$

We may further use this association that we see above, here:

$4000=4\cdot 1000=4\cdot 10^{3}$

Thus when we wish to express the Earth's mass, we may write:

$6000000000000000000000000\: units=\left \{ 24\: zeroes \right \}=$

$=6\cdot 10^{24}\: units$

Calculation works approximately along the same lines as that with decimals:

$0.1=\frac{1}{10}=\frac{1}{10^{1}}=10^{-1}$

$0.01=\frac{1}{100}=\frac{1}{10^{2}}=10^{-2}$

$0.001=\frac{1}{1000}=\frac{1}{10^{3}}=10^{-3}$

This association may be used thus:

$0.0005 =0.0001\cdot 5=5\cdot 10^{-4}$

The mass of hydrogen atom may be rewritten as:

$0.0000000000000000000000000017\: units=\left \{ 28\: zeroes \right \}$

$=1.7\cdot 10^{-28}\: units$

Video lesson

Write the following numbers using scientific notation:

5,210,000,000,000
0.000 000 000 000 000 23