SCIENTIFIC NOTATION
Scientists often work with very large and very small measurements. For example, the mass of
the Earth is about 6,000,000,000,000,000,000,000,000 kg and the mass of an electron is about
0.000 000 000 000 000 000 000 000 000 000 911 kg. Written in this form, the measurements
take up too much space and are difficult to use in calculations. To work with such numbers more
easily, we write them in a shortened form by expressing decimal places as powers of ten. This
method of expressing numbers is called exponential notation. Scientific notation is based on
exponential notation. In scientific notation, the numerical part of a measurement is expressed as
a number between 1 and 10, multiplied by a whole number power of 10. The general form looks
like this:
M x 10n
In this expression, M is the number greater than or equal to 1 and less than 10 and is referred to
as the mantissa. For example, two kilometers can be expressed as 2 x 103 m in stead of 2000 m.
The mass of a softball is about 1.8 x 10-1 kg.
To write measurements using scientific notation:
1. Move the decimal point until only one digit remains on the left (all non-significant zeros
must be dropped from the mantissa)
2. Count the number of places the decimal point was moved and use that number as the
exponent on the 10 (n).
 If you moved the decimal to the left to make the mantissa between 1 & 10 then the
exponent is positive.
o Thus the mass of the Earth can also be expressed as 6.0 x 1024 kg.
o 365 sec = 3.65 x 102 sec
 If you moved the decimal to the right to make the mantissa between 1 & 10 then the
exponent on the 10 is negative.
o Thus the mass of the electron can also be written as 9.11 x 10-31 kg.
o 0.007 kg = 7 x 10-3 kg
To rewrite a number into normal notation from scientific notation, reverse the process. For
example:
o 9.6 x 104 kg = 96,000 kg
o 6.3 x 10-4 m = 0.00063 m
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o 1 x 10 m = 1,000,000 m
o 9.50 x 10-7 sec = 0.000000950 sec
Practice Exercises:
Express the following measurements in scientific or normal notation & watch the significant
digits:
1) 5 800 m ________________________
7) 1.85 x 105 mi/s ___________________
2)
450 000 m ______________________
8)
3.02 x 108 m _____________________
3)
0.000 508 kg ____________________
9)
8.6 x 1010 mm ___________________
4)
0.000 000 45 mg _________________
10) 3.600 x 10-3 kg ___________________
5)
300 000 km/s ____________________
11) 4 x 10-8 kg ______________________
6)
0.000 301 0 L ____________________
12) 9.3 x 1010 mi ____________________
for more practice check out http://janus.astro.umd.edu/astro/scinote/
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