Scientists and other researchers may work with very large or astoundingly small numbers. Over the centuries, a special notation was developed for working with these kinds of numbers. It is called scientific notation.
Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a shorthand method for writing numbers, and an easy method for calculations.
For example, an astronomer is interested in the distances between the planets or stars. The dwarf planet, Eris, is about 8,900,000,000 miles from the sun. An astronomer could work with this in scientific notation as 8.9 X 109. If dealing with the mass of Earth, which is about 5,970,000,000,000,000,000,000,000 kilograms (kg), it is easier and more convenient to write it in scientific notation, 5.97 X 1024.
Standard notation is the way you write numbers every day. For example, 328,000 is a number in standard notation. The same number in scientific notation is as follows:
How is this conversion to scientific notation done? Actually it is very simple. It is written in three parts: the coefficient, the base and the exponent.
The three zeroes at the end of 328,000 are considered placeholders. They are dropped in scientific notation. The numbers before these placeholders are considered significant digits and are always kept.
A decimal is placed after the first significant digit, which is the three in this case. That significant digit is multiplied by 10 (the base) to the power of (exponent) a number that signifies the number of spaces the decimal was moved. In other words, you moved the decimal five places to the left from 328,000 to 3.28. So to make up for losing the five places after the significant digit, multiply that significant digit by 10 to the fifth power (105), since 105 = 100,000. Double-check the math:
3.28 x 105 = 3.28 x 100,000 = 328,000
To Write a Number in Scientific Notation
A number in scientific notation is in the form a x 10n, where 1 ≤ a < 10 and n is an integer.
If the number is greater than one,
Move the decimal point to the right of the first non-zero digit.
Drop all zeros behind the number.
Count the number of places you moved the decimal.
Write x 10 to this number of places written as a positive power behind the first number.
If the number is less than one,
Move the decimal point to the right of the first non-zero digit.
Drop all zeros in front of the number.
Count the number of places you moved the decimal.
Write x 10 to this number of places written as a negative power behind the first number.
Example 1: Writing Standard Notation in Scientific Notation
Write each of the numbers in scientific notation.
20,310,000
Move the decimal to the right of the first non-zero digit, which is two.
Count seven places that the decimal was moved, write this as the exponent, and drop the four zeros at the end.
0.000301
Move the decimal to the right of the first non-zero digit, which is three.
Count four places that the decimal has been moved, write this as a
negative exponent, and drop the zeros in front of the number.
Practice
The Richter scale measures an earthquake’s magnitude. Column four of this table shows the amount of energy released by an earthquake for each number on the scale. Convert the numbers in columns two and four to scientific notation.
Practice
To Write a Number in Scientific Notation
