1. Scientific Notation Unit 1, Lesson 6

2. The Basics Scientific Notation means expressing numbers (usually very large numbers or very small numbers) in the following form: a number between1 and 10 times 10 to an exponent such as: 2.3 X 10 4 4.76 X 10 -3 12.3 X 10 9 isn’t in scientific notation because 12.3 isn’t between 1 and 10

3. Converting from Decimal to Scientific Notation Simple rule: moving a decimal to the “right” means the exponent is negative; moving to the “left” means the exponent is positive Ex. 1 Put 0.000458 into scientific notation: First, move the decimal to the right 4 places  4.58 Second, moving to the right means a neg. exponent and the exponent is the same as the places moved  4.58 x 10 -4

4. Converting from Decimal to Scientific Notation Ex. 2 Put 1,256,008 into scientific notation Note: every number has a decimal point; if the number is an integer, the decimal is at the end even if it isn’t written So for 1,256,008 the decimal is to the right of the 8 First, move the decimal to the left 6 places  1.256008 Second, moving to the left means a positive exponent  1.256008 X 10 6

5. Converting from Scientific Notation to decimal form Same rule, just in reverse: If the exponent is negative, move the decimal to the left If the exponent is positive, move the decimal to the right Ex.1 3.06 X 10 -4 Negative exponent means move to the left (the number gets smaller); move decimal the same number of places as the exponent 3.06 X 10 -4 =.000306

6. Converting from Scientific Notation to decimal form Ex. 2 Write 8.7103 X 10 8 in decimal form First, a positive exponent means the decimal will be moved to the right; the “number” gets bigger. Note: Add zeros as needed when moving the decimal 8.7103 X 10 8 = 871,030,000

7. Practice Write in Scientific notation a)0.00056 = 5.6 X 10 -4 b)405 = 4.05 X 10 2 c)6741.38 = 6.74138 X 10 3 d).7065 = 7.065 X 10 -1

8. Practice Write in decimal form: a)3.07 X 10 -5 =.0000307 b)3.07 X 10 4 = 30,700

9. Computing with Scientific Notation To multiply numbers written in scientific notation, keep in mind the rules for exponents: With same base (10 in this case), add the exponents. Ex. 1: Simplify (3.5 X 10 4 )(6.7 X 10 -3 ) First, multiply the 3.5 and 6.7 = 23.5 Second, add the exponents  10 4 X 10 -3 = 10 1 Next, put them together  23.5 X 10 1 Finally, notice that the decimal needs to be moved and the exponent adjusted accordingly  2.35 X 10 2

10. Computing with Scientific Notation