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Unfortunately, academic numbers aren’t as manageable as in most math books.
Very big, as well as very small numbers can occur.
Example:
The distance between the earth and sun is 150 000 000 km.
Example
2: The mass of a hydrogen atom (that is about the smallest thing humans know
about) is 0,000 000 000 000 000 000 000 001 674 g.
But who
wants to write such long numbers all the time? You could say that the first
example is 150 gigameters but if you to write the number out nothing
changes. For the second example you say …. It’s also different. All the
zeros can be eliminated by mathematical expressions.
For 100
you could say: 10 ∙ 10 or 102
For 1 000
you could say 10 ∙ 10 ∙ 10 or 103
That’s
easy. 1 000 has three zeros and so 10 to the power of three is
1 000.
So 15 ∙
107 is 15 with 7 zeros. The ten is omitted in some books and
calculators. Then it says that 157 is the distance between the
sun and the earth.
All the
zeros after the comma in example 2 are characterized by negative exponents.
You will learn how to calculate that in the 10th grade.
So the hydrogen atom is:
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