Scientific notation

From Wiki4CAM

Scientific notation is a clear and handy way to express numbers. All numbers are written as a number between 1 and 10, multiplied by a power of ten.

Examples:

• The approximate population of the United States, 300 million, is written 3 x 10⁸
• Avogadro's number, the number of carbon atoms in 12 grams of pure carbon, is 6.022 x 10²³ (this is also defined as the number of atoms or molecules in a "mole" of a substance)
• One second is the 1/3600th part of an hour, or 0.000277..., written 2.77 x 10^-4
• One quarter (1/4) is written 2.5 x 10^-1

These are read, for example, "two point five times ten to the minus one".

The number of decimal places used corresponds to the accuracy of the number or measurement.

To multiply numbers in this notation, simply multiply the decimal number parts and round off to the appropriate accuracy, and add the exponents. If the result of the multiplication is 10 or greater, or less than 1, move the decimal point and alter the exponent accordingly. Moving the decimal point to the left increases the exponent and moving it to the right decreases the exponent.

Example: if the average American weighs 180 pounds, how many pounds do they weigh combined? 3 x 10⁸ times 1.80 x 10² = 5.4 x 10¹⁰

To divide numbers, simply divide the decimal number parts and round off to the appropriate accuracy, and subtract the exponents. If the result of the multiplication is 10 or greater, or less than 1, move the decimal point and alter the exponent accordingly. Moving the decimal point to the left increases the exponent and moving it to the right decreases the exponent.

Example: if there are 15 homeopathic practitioners for every 10,000 Americans, how many are there in the country? First, 10,000 = 1 x 10⁴. 3 x 10⁸ divided by 1 x 10⁴ = 3/1 x 10^8-4 = 3 x 10⁴. Multiplied by 15, we get 45 x 10⁴ = 4.5 x 10⁵ (450,000).