Unit 2- Measurements- Significant Figures & Scientific Notation

Significant Figures Figures (values) that indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

Counting Sig Figs Count all numbers EXCEPT: Leading zeros: Trailing zeros without a decimal point: 2,500  2 sig figs

Atlantic-Pacific Method Pacific Ocean “_________” Atlantic Ocean “ _______” PRESENT ABSENT

Atlantic-Pacific Method: Decimal point is PRESENT: count significant figures from the LEFT (Pacific side) Decimal point is ABSENT: count significant figures from the RIGHT (Atlantic side) Start counting significant figures at the first nonzero number and don’t stop until there are no more digits.

Practice Counting Sig Fig 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080 5. 0.006700 5. 0.006700 4 sig figs

Practice Counting Sig Fig Round the number at left to the number of significant figures stated in each column Number 4 sig figs 3 sig figs 2 sig figs 1 sig fig 80.405 29,350 80.41 80.4 80. 80 29,350 29,400 29,000 30,000

Multiplying & Dividing : Calculating Rules: Multiplying & Dividing : The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 3 SF 4 SF 3 SF 324 g

Calculating Rules: Adding & Subtracting: The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g

Significant Figures Practice Problems 85.6 cm 38 g 1.13 g

M x 10n 1 ≤ M < 10 +n: large # -n: small # Scientific Notation In science, numbers can be very small & very large (confusing!) Numbers can be expressed in Scientific Notation: M x 10n 1 ≤ M < 10 +n: large # -n: small #

Scientific Notation 65,000 kg  6.5 × 104 kg To convert into Sci. Notation: Move decimal until there’s 1 digit to its left. (# of places moved = exponent) Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs. 65,000 kg  6.5 × 104 kg

Scientific Notation Practice Problems 1. 2,400,000 mg 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm 2.4  106 mg 2.56  10-3 kg 0.00007 km 62,000 mm

Calculating with Scientific Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 2nd EE 2nd EE 5.44 7 8.1 4 ÷ ENTER = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol