A. Scientific Notation
Scientific notation is a convenient and precise way for engineers and scientists to represent very large and very small numbers. For example, the number 4,120,000 written in scientific notion is 4.12 × 106. The rules for scientific notation are given in Figure A-1.
In this example, we moved the implied decimal point from the right end of 4,120,000 six places to the left. By doing this, we divided the large number by one million so we have to multiply by a million, which is 10 × 10 × 10 × 10 × 10 × 10 or 106 to keep ourselves honest!
By the Way
In some cases, in displays that cannot show exponents (superscripts), the scientific notational number 4.12 × 106 is shown as 4.12e6. The “e” stands for exponent.
Table A.1 gives a few examples of numbers in scientific notation.
In scientific notation, it’s easy to convert a number that’s greater than 1 back to its long form as we show in Figure A-2. You write the number’s decimal digits and move the decimal point to the right by the number of places specified by the original number’s exponent, appending zeros where necessary.
Figure A-3 shows how to convert a number in scientific notation that’s less than 1 back to its long form. There, we write the number’s decimal digits and move the decimal point to the left by the number of places specified by the original number’s exponent, inserting zeros where necessary.
Scientific notation may not look too convenient, but indeed it is. Table A.2 gives a few examples of real-world physical constants in scientific notation.
By the Way
All of the notation above is strictly English notation. Other languages have different numerical notation. For example, in the German language the numerical meanings of periods and commas are reversed from what they mean in English. The English number 3,425,978.64 is written as 3.425.978,64 in German. In our English scientific notation, that number is 3.42597864 × 106.