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 exponent Small # (<1)  negative exponent

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

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

4. Practice
1) 5.21 x x 103 =
5.9 x 104
2) 9.55 x 1014 / x 106 =
2.85 x 108
3) x 105 x 2.01 x 108 =
1.70 x 1014
4) 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 V = 825 cm3 M = DV D = 13.6 g/cm3 M = (13.6 g/cm3)(825cm3)
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. Density D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL
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
WORK:
V = M D
V = g
0.87 g/mL
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. Dimensional Analysis cm in 8.0 cm 1 in 2.54 cm = 3.1 in
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in
8.0 cm
1 in
2.54 cm
= 3.1 in

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

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

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

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

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