Briefly describe scientific notation. how is it useful for writing large and small numbers? how is it useful for making approx
1 answer:
Scientific notation, also called pattern or notation in exponential form, is a way of writing numbers that accommodate values too large (100000000000) or small (0.00000000001) to be written in a conventional manner.
The use of this notation is based on powers of 104
Example:
Big numbers:
Small numbers:
However, in areas such as physics and chemistry, scientific notation is important to make approximations such as:
mass of a proton
mass of an electron and others.
The use of this notation is based on powers of 104
Example:
Big numbers:
Small numbers:
However, in areas such as physics and chemistry, scientific notation is important to make approximations such as:
mass of a proton
mass of an electron and others.
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It depends on what you mean by the delimiting carats "^"...
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
.
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
, so that 
. Then
which simplifies to
Now, recall that
. But we want the substitution we made to be reversible, so that
which implies that
. (This is the range of the inverse sine function.)
Under these conditions, we have
, which lets us reduce 
. Finally,
and back-substituting to get this in terms of
yields
Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for
In that case, you want to find the antiderivative,
Complete the square in the denominator:
Now substitute
which simplifies to
Now, recall that
which implies that
Under these conditions, we have
and back-substituting to get this in terms of