# E notation

## 1999-09-03

Dear Professor Mean, In my regression output, I saw that following value: -2.384E-03. What does this E notation mean?

Think of the “E” as short for extreme. Some numbers are very small, such as

0.0000000000000000000000016727

the weight of a proton in grams. Other numbers are very large, such as

5,913,520,000

the number of kilometers from the Sun to Pluto. In both cases it is difficult for a computer to display this number in a fixed amount of space. We can save some space by representing the number as a value between 1 and 10 times a power of ten. For example, the two numbers listed above could be represented as 1.6727*10^-24 and 5.91352*10^9.

The “E” is shorthand for multiply the number on the left by 10 raised to the power of the number on the right. We refer to this as scientific notation.

The value following the E tells you how many decimal places to shift your answer. If the value is negative, shift to the left. If the value is positive, shift to the right. So, the value -2.384E-03 means to shift the decimal three places to the left. When we do this, we get

-0.002384

Let’s suppose that SPSS displayed a very large number as 3.452E6. We would move the decimal 6 places to the right to get

3,452,000

If you want to find out more about scientific notation, check out the following web site.

1. Scientific Notation in Everyday Life.
Philip Spencer (accessed on July 27, 2001)
http://www.math.toronto.edu/mathnet/plain/questionCorner/scinot.html

You can find an earlier version of this page on my original website.