scientific notation converting into sci. notation: converting into sci. notation: move decimal...
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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