Scientific Notation

Converting into Sci. Notation:Converting into Sci. Notation:

Move decimal until there’s 1 digit to its Move decimal until there’s 1 digit to its left. Places moved = exponent.left. Places moved = exponent.

Large # (>1) Large # (>1) positive exponent positive exponentSmall # (<1) Small # (<1) negative exponent negative exponent

65,000 kg 6.5 × 104 kg

Scientific Notation

7. 7. 2,400,000 2,400,000 gg

8. 8. 0.00256 kg0.00256 kg

9.9. 7 7 10 10-5-5 km km

10.10. 6.2 6.2 10 1044 mm mm

Practice Problems

2.4 2.4 10 1066 gg

2.56 2.56 10 10-3-3 kg kg

0.00007 km0.00007 km

62,000 mm62,000 mm

Scientific Notation

Calculating with Sci. NotationCalculating with Sci. Notation(5.44 × 10(5.44 × 1077 g) ÷ (8.1 × 10 g) ÷ (8.1 × 1044 mol) = mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

Practice 1) 5.21 x 101) 5.21 x 1044 ++ 6.7 x 10 6.7 x 1033 = = 5.9 x 105.9 x 1044 2) 9.55 x 102) 9.55 x 1014 14 // 3.354 x 10 3.354 x 106 6 = = 2.85 x 102.85 x 1088

3) 8.467 x 103) 8.467 x 1055 x 2.01 x 10 x 2.01 x 108 8 = = 1.70 x 101.70 x 101414

4) 7.668 x 104) 7.668 x 1077 –– 3.4 x 10 3.4 x 1088 = = -2.63 x 10-2.63 x 1088

Density Density = mass per unit volumeDensity = mass per unit volume

Units for density: g/cmUnits for density: g/cm33 or g/mL or g/L or g/mL or g/L (solids) (liquids)(solids) (liquids) (gas) (gas)

D = MV

Density An object has a volume of 825 cmAn object has a volume of 825 cm33 and a density and a density

of 13.6 g/cmof 13.6 g/cm33. Find its mass.. 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

V

MD

Density A liquid has a density of 0.87 g/mL. What A liquid has a density of 0.87 g/mL. What

volume is occupied by 25 g of the liquid?volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

3

3

cm

gcm

Dimensional Analysis

The “Factor-Label” MethodThe “Factor-Label” Method Units, or “labels” are canceled, or Units, or “labels” are canceled, or

“factored” out“factored” out

g

Dimensional Analysis Steps:Steps:

1. Identify starting & ending units.1. Identify starting & ending units.

2. Line up conversion factors so units 2. Line up conversion factors so units cancel.cancel.

3. Multiply all top numbers & divide by 3. Multiply all top numbers & divide by each bottom number.each bottom number.

4. Check units & answer.4. Check units & answer.

Dimensional Analysis

5) Your European hairdresser wants to cut your hair 8.0 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?cm shorter. How many inches will he be cutting off?

8.0 cm8.0 cm 1 in1 in

2.54 cm2.54 cm= 3.1 in= 3.1 in

cm in

Dimensional Analysis

How many milliliters are in 1.00 quart of How many milliliters are in 1.00 quart of milk?milk?

1.00 qt1.00 qt 1 L1 L

1.06 qt1.06 qt= 943 mL= 943 mL

qt mL

1000 mL1000 mL

1 L1 L

Dimensional Analysis

6) Taft football needs 550 cm for a 1st 6) Taft football needs 550 cm for a 1st down. How many yards is this?down. How many yards is this?

550 cm550 cm 1 in1 in

2.54 cm2.54 cm= 6.0 yd= 6.0 yd

cm yd

1 ft1 ft

12 in12 in

1 yd1 yd

3 ft3 ft

Dimensional Analysis

You have 1.5 pounds of gold. Find its volume in You have 1.5 pounds of gold. Find its volume in cmcm33 if the density of gold is 19.3 g/cm if the density of gold is 19.3 g/cm33..

lb cm3

1.5 lb1.5 lb 1 kg1 kg

2.2 lb2.2 lb= 35 cm= 35 cm33

1000 g1000 g

1 kg1 kg

1 cm1 cm33

19.3 g19.3 g

Dimensional Analysis

Convert 75.0 inConvert 75.0 in33 to cm to cm33

2.54 cm = 1 in, so 16.387064 cm2.54 cm = 1 in, so 16.387064 cm33 = 1 in = 1 in33

75.0 in75.0 in33 16.387064 cm16.387064 cm33

1 in1 in33

= 1230 cm= 1230 cm33

Dimensional Analysis

Convert 35.0 mi/hr to m/minConvert 35.0 mi/hr to m/min (1609 m = 1 mile)(1609 m = 1 mile)

35.0mi = 35.0mi =

1 hr1 hr 1 mi1 mi

1609 m1609 m

60 min60 min

1 hr1 hr 939 m/min939 m/min