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

Next Class: Exponents and exponential functions, Exponential growth functions

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