# arrow_back Why do mathematicians use the scientific notation?

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Why do mathematicians use the scientific notation?

A shorthand method of writing very small and very large numbers is called scientific notation, in which we express numbers in terms of exponents of 10 . To write a number in scientific notation, move the decimal point to the right of the first digit in the number. Write the digits as a decimal number between 1 and $10 .$

Count the number of places $n$ that you moved the decimal point. Multiply the decimal number by 10 raised to a power of $n .$ If you moved the decimal left as in a very large number, $n$ is positive. If you moved the decimal right as in a small large number, $n$ is negative.

For example, consider the number $2,780,418$. Move the decimal left until it is to the right of the first nonzero digit, which is 2 .
We obtain $2.780418$ by moving the decimal point 6 places to the left. Therefore, the exponent of 10 is 6, and it is positive because we moved the decimal point to the left. This is what we should expect for a large number.
$$2.780418 \times 10^{6}$$

Working with small numbers is similar. Take, for example, the radius of an electron, $0.00000000000047 \mathrm{~m}$. Perform the same series of steps as above, except move the decimal point to the right.

Be careful not to include the leading 0 in your count. We move the decimal point 13 places to the right, so the exponent of 10 is $13 .$ The exponent is negative because we moved the decimal point to the right. This is what we should expect for a small number.
$$4.7 \times 10^{-13}$$

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