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Quick Reference
Chemistry
Scientific Notation
Scientific notation is very helpful when writing and working with extremely large or extremely
small numbers.
Numbers written in scientific notation are always written in the form a × 10b
For example, instead of writing 2350000000, one could write it in scientific notation as 2.35 × 109 .
This saves space and makes calculations simpler. The 9 in the exponent indicates that to get back
to the number in decimal notation(with all the zeros), the decimal point would be moved 9 places
to the right.
Large Numbers: For large numbers given in decimal notation, count how many decimal places
to the left the decimal point needs to be shifted in order for there to be one non-zero digit to the
left of the decimal point. This gives the exponent that goes above the 10.
For the number 458000, the decimal point would need to be shifted five places to the left to
leave only the 4 on the left side of the decimal point.
So, 458000 can be written as 4.58 × 105
458000 = 4.58 × 105
and
320 = 3.2 × 102
2.35 × 109 = 2350000000
Small Numbers: For a small number such as 0.00347, the exponent above the 10 is a negative
number whose absolute value is the number of decimal places that the decimal point would need
to be shifted to the right in order for there to be one non-zero digit to the left of the decimal point.
For 0.00347, if the decimal point were shifted three places to the right, the number would be
3.47. So,
0.00347 = 3.47 × 10−3
0.00000087 = 8.7 × 10−7
3.0 × 10−4 = 0.0003
Addition/Subtraction with Scientific Notation: When performing addition or subtraction
with two numbers that are in scientific notation, rewrite the numbers so that the exponent above
the 10 is the same for both numbers.Then perform the operation. Then rewrite the answer in
proper scientific notation.
For example
2.3 × 106 + 4.73 × 104 = 230 × 104 + 4.73 × 104
= (230 + 4.73) × 104
= 234.73 × 104
= 2.3473 × 106
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Enhanced Learning Center
Quick Reference
Chemistry
Sometimes it is simplest to rewrite both numbers such that the exponent is 0. This is the same as
decimal notation.
7.8 × 10−3 − 2.1 × 102 = 0.0078 × 100 − 210 × 100
= 0.0078 − 210
= −209.9922
= −2.09922 × 102
Multiplying in Scientific Notation: When multiplying together two numbers written in scientific notation, multiply the two numbers before the powers of 10 the way that you would if they
were written in decimal notation. Then add together the exponents above the 10.
For example,
(2.3 × 102 ) · (4 × 103 ) = (2.3 · 4) × 102+3
= 9.2 × 105
Also,
(4.7 × 109 ) · (3.2 × 10−4 ) = (4.7 · 3.2) × 109+(−4)
= 15.04 × 109−4
= 15.04 × 105
= 1.504 × 106
Dividing in Scientific Notation When dividing two numbers that are written in scientific notation, divide the two numbers before the powers of 10 the way that you would if they were written
in decimal notation. Then subtract the bottom power of ten from the top power of ten.
For example,
(6.4 × 105 )
(3.2 × 102 )
6.4
× 105−2
3.2
= 2 × 103
=
Another example:
(9 × 103 )
(3 × 105 )
9
× 103−5
3
= 3 × 10−2
=
Contributed by Sarah Withem, E.L.C. Tutor
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