Lab 1: Scientific Notation
Scientific Notation
We will be using scientific notation a lot in this class. For example, the mass of the Earth
is 5,979,000,000,000,000,000,000,000,000 kilograms and the molecular diameter of
ammonia is 0.0000000297 centimeters. These very large and small numbers are to
difficult to write without making an error. To prevent errors, these numbers can be
written in scientific notation. Basically, numbers are written as the product of a power of
10 and a number greater than or equal to 1, but less than 10. The mass of the Earth in
scientific notation is 5.979 x 10
27
kg and the molecular diameter of ammonia is 2.97 x 10

8
cm.
The simplest method for conversion of standard notation to scientific notation is move
the decimal. For very large numbers, move the decimal to the left, until it is after the first
numeral. Count the number of places the decimal has moved. This then becomes the
exponent on the 10. For example, write 4,567,000 using scientific notation.
4,567,000 becomes 4.567000
The decimal place has been moved 6 places to the left, so our exponent is 6.
The result: 4,567,000 = 4.567 x 10
6
For very small numbers, move the decimal to the right, until it is after the first nonzero
numeral. Count the number of places the decimal has moved. This becomes a negative
exponent on the 10. For example, write 0.00000005436 using scientific notation.
0.00000005436 becomes 00000005.436
The decimal place has been moved 8 places to the right, so our exponent is 8.
The result: 0.00000005436 = 5.436 x 10
8
To convert scientific notation to standard notation, reverse the procedure given above.
For very large numbers positive exponent on the 10), move the decimal to the right the
same number of places as given by the exponent. For very small numbers (negative
exponent on the 10), move the decimal to the left the same number of places as given by
the exponent. For example, write 7.943 x 10
6
and 4.302 x10
7
using standard notation.
7.943 x 10
6
= 7,943,000
4.302 x10
7
= 0.0000004302
Here are more examples.
..
10000 = 1
x 10
4
1/10 = 0.1 = 1 x
10

1
100028 =
1.00028 x 10
5
0.32 = 3.2 x 10

1
(not
usually done)
1000 = 1
x 10
3
1/100 = 0.01 = 1
x 10

2
24327 = 2.4327 x
10
4
0.053 = 5.3 x 10

2
100 = 1 x 1/1000 = 0.001 = 7354 = 7.354 x
0.0078 = 7.8 x 10

3