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Integer, Scientific Notation, Logarithm

Slide 22

March 2010

In the table shown here, each row shows the same value in 3 different numbering schemes: integer, scientific notation, and log-based 10. The first column is integers, which we know and love. We grew up with 1, 2, 3, 4, 5, etc. In the middle column is scientific notation. This is a short-hand way to save writing a lot of digits when a large number is involved. So, 1000 becomes 1.0 x 10 to the third power. This lets us know to put 3 zeroes behind the 1. In the log scale, 1000 is 3. You may notice that the exponent 3 from scientific notation is helpful when thinking in log. This is often helpful to some extent. The second row, one million, has 6 zeroes, so scientific notation is 1.0 x 10 to the sixth power. In log with a base of 10, the value is 6.

Now let's look at the blue text below the table. Log numbers use different "bases," the most common of which is ten. What this means is that the value of the log, in this case, 3, is used as the exponent for the base. In other words, 10 to the third power is 1000. We can write this out as 10 times 10 times 10.

In the second example, the base is 2. If we raise 2 to the power of 3, we have 2 times 2 times 2, equals 8.

In the third example, we would raise the base 10 to the 3.74 power. This one is harder to write out, but the result is that the log of the integer 5,500 is 3.74. In the last row of the table, you can see how this value differs from that of scientific notation.

Integer, Scientific Notation, Logarithm

 


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