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Scientific Notation


You often encounter very large and very small numbers in Chemistry. Writing them out in full can be very time consuming and can lead to text which is difficult to read. Instead, scientific notation (also called exponential notation) is used. Numbers are expressed in the form:
N x 10n
where N is a number between 1 and 10 and n is the exponent.

Large numbers - positive exponents


Written long hand, Avogadro's number is
60 220 000 000 000 000 000 000
In scientific notation, it becomes
6.022 x 1023 (read "six point zero two two times ten to the twenty-three")
The exponent tells us how many times the number 6.022 is multiplied by 10 to give the long form.

Alternatively, you can think of the exponent as the number of times the decimal point in the long hand form must be moved to the left in order to obtain a number between 1 and 10:
One million = 1000000.0
You must move the decimal point 6 places to the left to give the number 1.
In scientific notation, one million is 1.0 x 106

Small numbers - negative exponents


Written long hand, the mass of a hydrogen atom is
0.000 000 000 000 000 000 000 000 001 66
In scientific notation, it becomes
1.66 x 10-27 (read "one point six six times ten to the minus twenty-seven")
The negative exponent tells us how many times the number 1.066 is divided by 10 to give the long form.

Alternatively, you can think of the exponent as the number of times the decimal point in the long hand form must be moved to the right in order to obtain a number between 1 and 10.
One millionth = 0.000001
You must move the decimal point 6 places to the right to give the number 1.
In scientific notation, one million is 1.0 x 10-6

Scientific notation on calculators


Your scientific calculator should have a key labelled 'EXP' (occasionally 'EE') for entering numbers in scientific notation.
To enter the number "6.022 x 1023", you need to press the following sequence:
To enter the number "1.66 x 10-27", you need to press the following sequence with the '+/-' button used to change the sign of the exponent to negative:
The output is given in one of two formats depending on the calculator type. On some calculators, the number is displayed with the full scientific notation. On others, the display will show a number, a space and then the exponent. Both formats are shown above.

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