1.7 Scientific Notation

1. 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.

2. 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.

3. Example 1: • Write each number in decimal notation: • A) -2.6 x 109 • B) 3.017 x 10-6

4. Example 2: • Write each number in scientific notation: • A) 5, 210, 000, 000 • B) -0.00000006893

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

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

7. Example 4: • Perform the indicated computations, writing the answers in scientific notation: • A) (7.1 x 105)(5 x 10-7)

8. Example 4 continued . . . • B) 1.2 x 106 3 x 10-3

9. Example 5: • In 2004, the U.S. government collected 2.02 x 1012 dollars in taxes. At that time, the U.S. population was approximately 295 million or 2.95 x 108. Find the per capita tax, rounded to the nearest dollar, in 2004.

10. Example 6: • A futuristic spacecraft traveling at 1.55 x 103 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)

11. Homework: • Page 82 1 – 57 every other odd 15 total