Scientific measurements often produce long numbers. Consider the speed of light, which is 3,000,000,000 m/sec, or the mass of a dust particle, which is 0.000000000753 kg. Scientific notation is a method of writing long, standard numbers in a condensed format based on powers of 10. Using scientific notation, the speed of light (3,000,000,000 m/sec) is written as:
3.00 x 10^{9} m/sec
The first number (3.00) is called the coefficient. The coefficient must be between 1.00 and 9.99. The second number (10^{9}) is called the base. The base is always written in exponent form with positive exponents for numbers greater than or equal to 1.00, or negative exponents for numbers less than 1.00. Using scientific notation, the mass of a dust particle weighing 0.000000000753 kg is written as:
7.53 x 10^{-10} kg
Notice that the exponent is a negative number and the units remain the same.
Converting standard numbers to scientific notation requires four steps.
360000
3.60000
3.60000 x 10^{5}
3.6 x 10^{5} kg
Here is an example of converting a standard number less than 1.00 to scientific notation:
0.00023
00002.3
00002.3 x 10^{-4}
2.3 x 10^{-4} kg
Similarly, scientific notation can be converted to standard notation in four steps.
5.70 x 10^{-3} kg
10^{-3} indicates that the decimal will move 3 places to the left
5.70 becomes 0.00570
0.00570 kg
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