Scientific Notation Writing Large and Small Numbers

2 Scientific Notation Writing Large and Small Numbers 

Science has constantly pushed the boundaries of the very large and the very small. We can, for example, now measure time periods as short as 0.000000000000001 seconds and distances as great as 14,000,000,000 light-years. Because the many zeros in these numbers are cumbersome to write, scientists use scientific notation to write them more compactly In scientific notation, 0.000000000000001 is 1 X 10 and 14,000,000,000 is 1.4 X 10. A number written in scientific notation consists of a decimal part, a number that is usually between 1 and 10, and an exponential part, 10 raised to an exponent, n. 

To convert a number to scientific notation, move the decimal point (either to the left or to the right, as needed) to obtain a number between 1 and 10 and then multiply that number (the decimal part) by 10 raised to the power that reflects the movement of the decimal point. For example, to write 5983 in scientific notation, move the decimal point to the left three places to get 5.983 (a number between 1 and 10) and then multiply the decimal part by 1000 to compensate for moving the decimal point. 

You can do this in one step by counting how many places you move the decimal point to obtain a number between 1 and 10 and then writing the decimal part multiplied by 10 raised to the number of places you moved the decimal point. 

If the decimal point is moved to the left, as in the previous example, the exponent is positive. If the decimal is moved to the right, the exponent is negative. 

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Scientific Notation Writing Large and Small Numbers 12 2.5 The Basic Units of Measurement 22 2.10 Numerical Problem-Solving... 

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