Scientific notation

Scientific notation is a way of expressing a number as a coefficient multiplied by a power of 10. This is useful because many values in physics are either too large or too small to write as ordinary decimal numbers. The coefficient is a decimal number, greater than (or equal to) 1 but less than 10. Powers of 10 are 10−1 = 0.1, 100 = 1, 101 = 10, 102 = 100, and so on. For example, the number 1,500 is 1.5×103. The number 1.5 is the coefficient. The number 103 is a power of 10. The small, raised numeral 3 is the exponent. For the number 1,500, this may seem like more trouble than it is worth. But consider a very large number, such as the speed of light, which is 3 hundred million or 300,000,000 m/s. In scientific notation this is 3×108 m/s, which is much easier to write without making a mistake. Read the text aloud Show Typical values in physics
Scientific notation
For numbers less than one, scientific notation uses negative exponents. For example, the number 0.001 is 1 ÷ 1000 = 1 ÷ 103 = 10–3. A negative sign on the exponent of 10 does not mean that the number is negative! In scientific notation, negative exponents mean a value that is less than one. For example, the quantity 0.0025 m is 2.5×10–3 m. Read the text aloud
Scientific notation can also be represented by adding a prefix to the quantity. Two thousand meters is the same as 2×103 meters or 2 kilometers, where “kilo” means “one thousand” and is abbreviated “km.” The tables below show some useful prefixes. Read the text aloud
Prefixes in the metric system
Computers and scientific calculators use scientific notation. Instead of the multiplication sign (×) a computer uses the letter “E” and a calculator uses either “E” or “EE.” The letter “E” stands for exponential, which is another term for scientific notation. The diagram below shows how to enter scientific notation numbers on a calculator and computer. Pay close attention to the order in which you use the +/− key when you need to enter a negative exponent on a calculator! Read the text aloud
Using scientific notation on a calculator
Which of the following is equal to 32,000,000?
  1. 3.2×10−1 kiloseconds
  2. 3.2×101 megaseconds
  3. 3.2 gigaseconds
  4. 3.2×106 seconds

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