1. Measurement – The Metric System

2. A. SI Prefix Conversions
1. Find the difference between the exponents of the two prefixes.
2. Move the decimal that many places.
To the left
or right?

3. A. SI Prefix Conversions=
532 m = _______ km
0.532
NUMBER
UNIT
NUMBER
UNIT

4. A. SI Prefix Conversions
Symbol
Factor
mega- M
106
kilo- k
103
BASE UNIT
---
100
deci- d
10-1
move left
move right
centi- c
10-2
milli- m
10-3
micro- 
10-6
nano- n
10-9
pico- p
10-12

5. A. SI Prefix Conversions
0.2
1) 20 cm = ______________ m
2) L = ______________ mL
3) 45 m = ______________ nm
4) 805 dm = ______________ km 32
45,000
0.0805

6. 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

7. 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

8. 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

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

10. 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.

11. Dimensional Analysis qt mL 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL
How many milliliters are in 1.00 quart of milk? qt mL
1.00 qt
1 L
1.057 qt
1000 mL
1 L
= 946 mL 

12. 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

13. Dimensional Analysis in3 L 75.0 in3 (2.54 cm)3 (1 in)3 1 L 1000 cm3
How many liters of water would fill a container that measures 75.0 in3?
in3 L
75.0 in3
(2.54 cm)3
(1 in)3
1 L
1000 cm3
= 1.23 L

14. Dimensional Analysis cm in 8.0 cm 1 in 2.54 cm = 3.2 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
= 3.2 in

15. 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

16. M V D = Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L
Combination of base units.
Volume (m3 or cm3)
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
D = M V
Density (kg/m3 or g/cm3)
mass per volume

17. 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

18. 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

19. Percent Error your value accepted value
Indicates accuracy of a measurement
your value
accepted value

20. Percent Error % error = 2.9 %
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
% error = 2.9 %

21. ACCURACY
Accuracy can be defined as how close a number is to what it should be.
Accuracy is determined by comparing a number to a known or accepted value.

22. PRECISION Precision has two meanings
1. Repeatability : can you get the same result over and over

23. Precision can also mean
The number of decimal places assigned to the measured number (The more decimal places, the more precise the measurement)

24. Example 1: How old are you? I am 16 years old
I am 15 years and 8 months old
I am 15years, 8 months, and 5 days old
I am 15 years, 8 months, 5 days, and 10 hours old

25. Accuracy vs. Precision for Example 1
Each of these statements is more accurate and more precise than the one before it.
Statement two is more accurate and more precise that statement one.
Statement three is more accurate and more precise than statement two.

26. Example 2: How long is a piece of string?
Johnny measures the string at 2.63 cm.
Using the same ruler, Fred measures the string at 1.98 cm.
Who is most precise?
Who is most accurate?
The actual measurement is 2.65 cm.

27. Accuracy vs. Precision for Example 2
Johnny is fairly accurate and also very precise.
Fred is very precise, however, he is not very accurate. His lack of accuracy is due to using the ruler incorrectly.

28. ACCURACY/PRECISION
You can tell the precision of a number simply by looking at it. The number of decimal places gives the precision.
Accuracy on the other hand, depends on comparing a number to a known value. Therefore, you cannot simply look at a number and tell if it is accurate