1.7 Scientific Notation A number is written in scientific notation when it is expressed in the form where the absolute value of a is greater than or equal to 1 and less than 10, and n is an integer.

If n is positive, move the decimal point in a to the _______________ n places. If n is negative, move the decimal point in a to the _______________ places.

Example 1: Write each number in decimal notation: A) -2.6 x 10 9 B) x 10 -6

Example 2: Write each number in scientific notation: A) 5, 210, 000, 000 B)

Example 3: In 2005, the federal cost of social security was $519 billion. Express this amount in scientific notation.

Computations with Numbers in Scientific Notation Multiplication: (a x 10 n )(b x 10 m ) = (a x b) x 10 n + m Division: a x 10 n = a x 10 m - n b x 10 m b After the computation is completed, the answer may require an adjustment before it is back in scientific notation.

Example 4: Perform the indicated computations, writing the answers in scientific notation: A) (7.1 x 10 5 )(5 x )

Example 4 continued... B) 1.2 x x 10 -3

Example 5: In 2004, the U.S. government collected 2.02 x dollars in taxes. At that time, the U.S. population was approximately 295 million or 2.95 x Find the per capita tax, rounded to the nearest dollar, in 2004.

Example 6: A futuristic spacecraft traveling at 1.55 x 10 3 miles per hour takes 20, 000 hours (about 833 days) to travel from Venus to Mercury. What is the distance from Venus to Mercury? (Hint: d = rt)

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