Ch. 1 Scientific Notation and Sig Figs

Importance of scientific notation

Important for very large and very small values

Format

• Proper format

  • Coefficient or mantissa must be between 1 and 10 aka just one non-zero digit before decimal

  • Power of 10, positive exponent means BIG number, negative exponent means small number

• Example

  • 6.022 x 1023 = 602,200,000,000,000,000,000,000

• Example

  • 9.11 x 10-31= 0.000000000000000000000000000000911

Changing scientific notation

As mantissa increases, exponent must decrease and vice versa

Uncertainty

• All measurements have uncertainty (aka; slop, give or take, +/-, deviation, margin of error)

• The paper clip weighs 3.2 grams +/- .03 grams

• How to deal with uncertainty in calculation?

  • Calculus (adding delta’s)

• Statistical

  • (A +/- a) + (B +/- b) = (A+B) +/- (a2 + b2)1/2

  • Major hassle (even worse for multiplication)

• Sig Figs

To use sig figs you must be able to do what?

1. Count sig figs

2. Apply rules for addition/subtraction and multiplication/division

Counting sig figs

• A digit is significant if it was measured

• All non-zero digits are significant

• Zeroes are tougher; there are 4 types

  • Tweeners: 1.02 km (sig)

  • Trailing, right of decimal point: 6.90 mg (sig)

  • Leading, right of decimal point: .023 L (not sig)

  • Trailing, left of decimal point: 110 kg (not sig)

Determining the number of sig figs in a calculated anser

• Count the number of sig figs in the two measurements being combined.

  • If you’re multiplying or dividing, keep the smallest number of sig figs

    • 4 sig fig measurement x 6 sig fig measurement gives a 4 sig fig measurement

  • If you’re adding or subtracting, do the same thing for decimal places to the right of the decimal point.