SIG FIGS AND SCIENTIFIC NOTATION Let’s get the basics out of the way!

Remember Sig Figs??

Objective

  Review Sig Figs, Scientific Notation, Dimensional Analysis, and basic trig to make future physics problems easy!

  Worksheet Due Friday   Quiz Friday

SIG FIG REVIEW

  1. All non-zero numbers are significant.

  2. Any "sandwiched" zeroes are significant.

  3. Leading zeroes are NOT significant.

  4. Trailing zeroes are significant, ONLY if there is a decimal.

  Practice:   213   203   0.0023   230   230.   230.0

Math with SIG FIGs

  Multiplication and division (find the pattern)   2x3 = 6   2.0 x 3.0 = 6.0   2.0 x 3 = 6   100.00 / 50. = 2.0

Count Sig Figs. Round answer to least amount of sig figs.

Try These!

  7.00 x 8.0   2.0 x 0.5   36.0/18

Try These!

  7.00 x 8.0 = 56   2.0 x 0.5 = 1   36.0/18 = 2.0

Math with SIG FIGs

  Addition/Subtraction (find the pattern)   5 + 8 = 13   102 + 2 = 104   102.0 + 2.0 = 104.0   102.0 + 2 = 104   102 + 2.0 = 104   102.00 + 2.0 = 104.0   102.005 + 2 = 104

Count Sig Figs in decimal portion! Round answer’s decimal portion to the least amount of sig figs.

Try These!

  8.0+ 1.01   2,354 + 1.1   85.07+2.0

Try These!

  8.0+ 1.01 = 9.0   2,354 + 1.1 = 2,355   85.07+2.0 = 87.1

Why do we use Scientific Notation?

 Scientific notation is used in science to represent very large and very small numbers

Length of swine flu virus: diameter of 10 to 300 nanometers (nanometer is equal to one billionth of a meter) 0.0000000000001m becomes 1.0 x 10-13m

Scientific Notation

 Expresses a number as the product of a number between 1 and 10 and a power of 10

 Ex: 93,000,000 = 9.3 x 107

Numbers Larger than 1

 Numbers larger than 1 are expressed with a power of 10 that is positive

 602000000000000000000000 can be written as 6.02 x 1023

Numbers smaller than 1

 Numbers smaller than 1 are expressed with a power of 10 that is negative

  0.000 000 1 cm can be written 1.0 x 10-7 cm

1,500,000

1.5 x 106

0.00043

4.3 x 10-4

11.234

1.1234 x 101

Opposite Challenge: Write in Standard Notation

 7.8 x 10-5

0.000078

How do I enter numbers in scientific notation in my calculator?

 Most Important Rules:   -Use the exponent key instead of ^   -Always put numbers in ( )

Find the trend…

(2 x 103)(3 x 102) = 6.0 x 105

(1 x 105)(7 x 10-3) = 7 x 102

(4 x 106)(8 x 104) = 3.2 x 1011

What is the pattern here?

Multiplying Scientific Notation

Rules:   MULTIPLY the numbers   ADD the exponents

(3.2 x 103)(2.0 x 105) = 6.4 x 108

Find the trend…

8 x 106 = 2 x 104

4 x 102

9 x 105 = 3 x 109 3 x 10-4

1.8 x 10-3 = 2 x 10-11

9 x 107

Talk it out with your elbow partner – what is the pattern here?

Dividing Scientific Notation

Rules   DIVIDE the numbers   SUBTRACT the exponents

8 x 105 = 4 x 102 2 x 103

Addition and Subtraction

  To add or subtract in scientific notation, both numbers must have the same exponent!

  Then, add the numbers and leave the same power of ten.

  (2.3 x 103) + (5.12 x 105) =   (0.023 x 105) + (5.12 x 105) = (5.143 x 105)   SIG FIGS!   (5.14 x 105)

Metric Conversions

  We’ll use these often!

Basic Trig

  We will always use degrees!!!   SOH CAH TOA   What is sin(C)?   Sin(C)= 21/29

Find the missing side

  cos(27) = x / 20   X = 18

Find the missing angle

  Tan(x) = 10/33   Tan(x) = .30303   X = tan-1(0.30303)   X = 17o