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Scientific Notation

Scientific Notation. 65,000 kg  6.5 × 10 4 kg. Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10 -5 km

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Scientific Notation

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  1. Scientific Notation 65,000 kg  6.5 × 104 kg • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. • Large # (>1)  positive exponentSmall # (<1)  negative exponent

  2. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  3. EXE EXP EXP ENTER EE EE Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

  4. Practice • 1) 5.21 x 104+ 6.7 x 103 = • 5.9 x 104 • 2) 9.55 x 1014 / 3.354 x 106 = • 2.85 x 108 • 3) 8.467 x 105 x 2.01 x 108 = • 1.70 x 1014 • 4) 7.668 x 107– 3.4 x 108 = • -2.63 x 108

  5. M V D = Density • Density = mass per unit volume • Units for density: g/cm3 or g/mL or g/L (solids) (liquids) (gas)

  6. Density • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

  7. WORK: V = M D V = 25 g 0.87 g/mL Density • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g V = 29 mL

  8. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  9. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  10. cm in Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm 1 in 2.54 cm = 3.1 in

  11. qt mL  Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.06 qt 1000 mL 1 L 1.00 qt = 943 mL

  12. cm yd Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

  13. lb cm3 Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

  14. Dimensional Analysis • Convert 75.0 in3 to cm3 (2.54 cm)3 (1 in)3 75.0 in3 = 1230 cm3

  15. Dimensional Analysis 1 hr 1609 m 939 m/min 60 min 1 hr 1 mi • Convert 35.0 mi/hr to m/min • (1609 m = 1 mile) • 35.0mi =

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