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Published byScott Washington Modified over 8 years ago

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Scientific notation is a quick way of writing very large or very small numbers. Scientific Notation & Significant Digits Example #1 Write 234 000 000 m/s in scientific notation. 2.34 x 10 8 m/s. The decimal is moved until there is only one non-zero digit to the left. To show that the decimal has moved 8 places to the left, a positive exponent of 8 has been given to the base 10.

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Example #2 Write 0.000 000 000 478 s in scientific notation. 4.78 x 10 -10 s. The decimal has been moved 10 places to the right. A negative exponent of 10 has been given to the base.

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Significant Digits In any given number, some digits are significant, and some are not. To decide which digits are which a set of rules must be followed. All non-zero digits are significant. (ie. 374 has three significant digits) All leading zeros are not significant. (ie. 0.000 035 has 2 significant digits). If there is no decimal point, all trailing zeros are not significant. (ie 125 000 has three significant digits).

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All digits used in the coefficient of a number written in Scientific notation are significant. (ie. 3.500 x 10 3 has 4 significant digits). smallest The number of significant digits in the answer to a problem should always equal the smallest number of significant digits in the given data.

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Example #3 State the number of significant digits in each of the following. a) 564b) 2500c) 3.0 d) 1.350e) 0.005f) 2.00 x 10 2 g) 250 001h) 0.34i) 0.00 304 0

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Example #4 Round each of the following to 3 significant digits. a)2.375b) 6.7c) 5 d) 2e) 20f) 200

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