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:

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

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

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Video lesson

Write the following numbers using scientific notation:

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