### Scientific Notation

Scientific notation is a shorter way to write numbers that have lots of insignificant placeholder digits. Scientific notation expresses numbers as a product of powers of 10, with the form:

where y is a number typically between 1 and 10, and z is an integer exponent of 10 that indicates how many places the decimal point must be moved to accomplish this.

For example, the number 65000000 would be written 6.5 x 107. In this example y=6.5, which meets the requirement that 1<y<10, and z=7, since there are seven digits trailing the 6 and we must move the decimal point 7 places to the left:

When using scientific notation and significant digits, all of the significant digits and only the significant digits are listed. So, for the example of 6.5 x 107, there are two significant digits. As a second example, the number 123400 would be written 1.234 x 105, since there are five trailing digits after the 1. In this example, 123400 and 1.234 x 105 both indicate four significant digits.

Because only significant digits are included when using significant digits with scientific notation, this can eliminate the ambiguity of significant zeros. For the example of a 200 cm long branch in the previous section, we can write this as 2 x 102 to indicate one significant digit, 2.0 x 102 to indicate two significant digits, or 2.00 x 102 to indicate three significant digits.

To indicate numbers with absolute values of less than one, z is negative. For example, .0000987, converted to scientific notation, is 9.87 x 10-5, where -5 indicates that the decimal point has been moved 5 places to the right: