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Play and Review Scientific Notation The Metric System and Scientific Notation a simple explanation |
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Scientific NotationIn science, it is common to work with very large and very small numbers. For example, the diameter of a red blood cell is 0.0065 cm, the distance from the earth to the sun is 150,000,000 km, and the number of molecules in 1 g of water is 33,400,000,000,000,000,000,000. It gets cumbersome to work with such long numbers, so measurements such as these are often written using a shorthand called scientific notation.Each zero in the numbers above represents a multiple of 10. For example, the number 100 represents 2 multiples of 10 (10 x 10 = 100). In scientific notation, 100 can be written as 1 times 2 multiples of 10: 100 = 1 x 10 x 10 = 1 x 102 (in scientific notation) Scientific notation is a simple way to represent large numbers because the exponent on the 10 (two in the example above) tells you how many places to move the decimal of the coefficient (the one above) to obtain the original number. In our example, the exponent two tells us to move the decimal to the right two places to generate the original number:
Scientific notation can be used even when the coefficient is a number other than 1. For example:
This shorthand can also be used with very small numbers. When scientific notation is used with numbers less than one, the exponent on the 10 is negative, and the decimal is moved to the left, rather than the right. For example:
Therefore, using scientific notation, the diameter of a red blood cell is 6.5 x 10-3 cm, the distance from the earth to the sun is 1.5 x 108 km and the number of molecules in 1 g of water is 3.34 x 1022. A final note, in scientific notation, the base numeral is always represented as a single digit followed by decimals if necessary. Therefore, the number 0.0065 is always represented as 6.5 x 10-3, never as 0.65 x 10-2 or 65 x 10-4. Source: www.visionlearning.com |
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