Exponents and Scientific Notation

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Scientists often need to represent very small numbers and very large numbers which have many digits. These numbers can be so long that they are difficult to read. So, scientists developed a simpler method to represent these numbers, called scientific notation.

Scientific notation requires the use of exponents. An exponent is a number or symbol indicating how many times a base number should be multiplied by itself. For example, the “5” in 85 is an exponent and 85 can also be expressed as “eight to the power of five” or 8 x 8 x 8 x 8 x 8. When you write numbers using scientific notation, 10 is the always the base number. Each time you multiply by 10, you move the decimal point to the right one place. So, multiplying by 106 moves the decimal point to the right six places. Scientific notation takes a number between 0 and 10 and multiplies it by a power of 10, moving the decimal point to the left or right the correct number of places. Scientific notation is useful for writing very large numbers representing distances in space. For example, engineers designing a probe to send to Neptune would often need to refer to the distance between Earth and Neptune, which is 4,700,000,000.0 kilometers. 4,700,000,000.0 can be expressed as 4.7 with the decimal point moved to the right nine places. 4.7 x 109 km = 4,700,000,000.0 km

Very small numbers can also be written using scientific notation. For example, the diameter of a hydrogen atom is approximately 0.000000000106 meters. To write small numbers, you divide by 10 instead of multiplying by 10. You can represent this in scientific notation using negative exponents. 0.000000000106 meters is 1.06 meters with the decimal point moved to the left 10 times. 1.06 x 10-10 m = 0.000000000106 m

Rules for using scientific notation: • Always use a number between 0 and 10. • When writing decimal numbers, round up if the number to the right of it is 5 or greater. • Positive exponents move the decimal to the right. Fill in the spaces with zeros. • Negative exponents move the decimal to the left. Fill in the spaces with zeros.