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Scientific notation is a way to express numbers that are either very large or very small. In traditional notation the first kind would have a lot of 0s between the decimal point and the first significant figure whereas the second kind would have a large number of trailing 0s. The need for scientific notation arose from advances in various branches of science: physical particles, astronomical or cosmological distances, size of single cell animals. Nowadays, even non-scientific values such as population, national debts (of some countries) could usefully utilize scientific notation.
A number in scientific notation is written as a * 10b where 1 ≤ a < 10 (although a can be negative with the domain reversed) and b is an integer (negative or positive).
To convert a number to scientific notation:
· If the number has no decimal point, then add one at the end.
· Then move the decimal point to just after the first digit while counting the number of places you have moved it.
· The new number, formed after moving the decimal point is a.
· The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative.
For example:
23045.06 becomes 2.304506*104
0.00023004 becomes 2.3004*10-4
To convert a number in scientific notation to normal form:
· If b is positive, move the decimal point b places to the right in the number a - adding 0s at the end of the number, if required.
· If b is negative, move the decimal point b places to the left in the number a - adding leading 0s after the decimal point, if required.
For example:
4.56*105 = 456000.
4.56*10-5 = 0.0000456
I have avoided using the term "Standard form" because, ironically, it is a non-standard term. In the UK Standard and Scientific forms are the same whereas in the US, the Standard form is what I have chosen to call the normal form.
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∙ 10y ago
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