1. UNITS
Science makes all measurements using the metric system
Length Meter (m)
Mass Gram (g)
Volume Liter (L)
( = inches)
( = ounces)
( = quarts)
EX1-1 (of 29)

2. Prefix Symbol Base Unit Multiplying Factor giga G 109 mega M 106
METRIC PREFIXES
Prefix Symbol Base Unit Multiplying Factor
giga G
mega M 106
kilo k 103
BASE UNIT 100
Yippe-kai-ay,
BUMF
1 byte = bytes
1 m = m
1 g = g
John McClane
EX1-2 (of 28)

3. METRIC PREFIXES
Prefix Symbol Base Unit Multiplying Factor
giga G
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
EX1-3 (of 28)

4. Convert 525 meters into kilometers
An EQUALITY STATEMENT between meters and kilometers is needed
1 BIG km = 103 small m
____
100
1 km = 103 m
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
larger unit 
EX1-4 (of 28)

5. Convert 525 meters into kilometers
An equality statement can be written as a fraction called a CONVERSION FACTOR
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
103 m
_______
1 km
1 km
_______
103 m or
525 m
x 1 km
________
103 m
= km
EX1-5 (of 28)

6. Convert 0.170 grams into centigrams
1 BIG g = small cg
_____
10-2
1 g = 102 cg
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
0.170 g
x 102 cg
________
1 g
= cg
larger unit 
EX1-6 (of 28)

7. Convert 24.5 milliliters into liters
1 BIG L = small mL
_____
10-3
1 L = 103 mL
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
24.5 mL
x L
________
103 mL
= L
larger unit 
EX1-7 (of 28)

8. Convert 0.674 decimeters into micrometers
1 BIG dm = small μm
_____
10-6
1 dm = μm
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
0.674 dm
x 105 μm
_________
1 dm
= 67,400 μm
larger unit 
EX1-8 (of 28)

9. Convert 22.5 mL/s into L/min
1 BIG L = 103 small mL
1 min = 60 s
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
22.5 mL
___________ s
x 1 L
________
103 mL
x s
________
1 min
= L/min
EX1-9 (of 28)

10. Convert 187.0 J/hr into kJ/day
1 BIG kJ = 103 small J
1 day = 24 hr
METRIC PREFIXES
Prefix Symbol BUMF
giga G 109
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
187.0 J
__________ hr
x 1 kJ
_______
103 J
x 24 hr
________
1 day
= kJ/day
EX1-10 (of 28)

11. Tolerances: the expected variation
MEASUREMENTS
All measurements contain error because the last bit of each measurement must be estimated
6.8 cm
± 0.1 cm
6.80 cm
± cm
TOLERANCE – For a piece of equipment, it is the expected range of variation in a reading
Tolerances: the expected variation
for each ruler
EX1-11 (of 28)

12. MEASUREMENTS
All measurements contain error because the last bit of each measurement must be estimated
6.8 cm
6.7 to 6.9 cm
6.80 cm
6.79 to 6.81 cm
TOLERANCE – For a piece of equipment, it is the expected range of variation in a reading
Expected range
for the measured value
EX1-12 (of 28)

13. TOLERANCES OF GRADUATED EQUIPMENT
Tolerances are usually larger than ±1 in the last decimal place
Tolerances are often provided by the manufacturer
5-mL Volumetric Pipet : ± mL
50-mL Volumetric Buret : ± mL
100-mL Volumetric Flask : ± mL
A tolerance in the hundredths place means the measurement should be given to the hundredths place
Reading for a 5-mL Volumetric Pipet :
5.00 mL
Expected range for the measured value :
4.98 mL to mL
5.00 ± 0.02 mL
EX1-13 (of 28)

14. SIGNIFICANT FIGURES
Provide a method to insure answers to arithmetic operations with measurements maintain the same tolerance
SIGNIFICANT FIGURES – Every digit recorded in a measurement
(all certain digits plus one uncertain digit)
EX1-14 (of 28)

15. from the least reliable measuring device
59 cm 59.6 cm cm
59 cm 59.6 cm cm
58 to 60 cm
59.5 to 59.7 cm
59.62 to cm
2 sig fig’s
3 sig fig’s
4 sig fig’s
from the least reliable measuring device
from the most reliable measuring device
EX1-15 (of 28)

16. Significant figures are determined only for measurements
, not for
(1) Counted numbers
(28 students enrolled)
(2) Defined numbers
(1 km = 103 m)
EX1-16 (of 28)

17. RULES FOR COUNTING SIGNIFICANT FIGURES
(1) The first significant figure in a measurement is the first non-zero digit , 4 4 3
24.74 to 24.76
3,040 to 3,042 to
EX1-17 (of 28)

18. RULES FOR COUNTING SIGNIFICANT FIGURES
(2) Zeros that end a number with a decimal point are significant 3 2 3 3
(3) Zeros that end a number without a decimal point are not significant 1 2
EX1-18 (of 28)

19. A non-significant zero can be made significant with a bar over it
300 _
300 _
300
300.0 1 2 3 4
200 to 400
290 to 310
299 to 301
299.9 to 300.1
EX1-19 (of 28)

20. 3 5 3 2
,019 43,100 1 4 4 3 1, 4 3 5 4
EX1-20 (of 28)

21. When writing a measurement in scientific notation, only significant figures are shown _
6.8 × 102
6.80 × 102
6.800 × 102
EX1-21 (of 28)

22. ADDING AND SUBTRACTING MEASUREMENTS
Approximate technique – The answer’s last digit will be in the same place as the last digit in the least accurate addend
20.63 mL
+ 6.6 mL
Last sig fig: hundredths place
Last sig fig: tenths place
27.23 mL
27.2 mL
Last sig fig must be in the tenths place
← Correct answer
EX1-22 (of 28)

23. ADDING AND SUBTRACTING MEASUREMENTS
Approximate technique – The answer’s last digit will be in the same place as the last digit in the least accurate addend
1,840 km
+ 576 km
Last sig fig: tens place
Last sig fig: ones place
2,416 km
2,420 km
Last sig fig must be in the tens place
← Correct answer
EX1-23 (of 28)

24. ADDING AND SUBTRACTING MEASUREMENTS
Exact technique – The answer’s tolerance is the sum of the tolerances of each measurement
± g
± g
± g
± g
← Give the tolerance to only one digit g
± 0.05
← Last sig fig must match the tolerance
EX1-24 (of 28)

25. MULTIPLYING AND DIVIDING MEASUREMENTS
Approximate technique – The number of sig fig’s in the answer will equal the number of sig fig’s in the factor with the least number of sig fig’s
(2.41 m)(0.25 m)
= m2
Answer = m2
Sig Fig’s: 3 2
Answer will have 2 sig fig’s
EX1-25 (of 28)

26. MULTIPLYING AND DIVIDING MEASUREMENTS
Approximate technique – The number of sig fig’s in the answer will equal the number of sig fig’s in the factor with the least number of sig fig’s
617.4 m ÷ s
= 1,234.8 m/s
Answer = 1,200 m/s
Sig Fig’s: 4 2
Answer will have 2 sig fig’s
EX1-26 (of 28)

27. MULTIPLYING AND DIVIDING MEASUREMENTS
Exact technique – The answer’s RELATIVE tolerance is the sum of the RELATIVE tolerances of each measurement
(0.313 ± L)(44.30 ± 0.03 atm)
____________________________________________
( ± L)
= atm =
________
0.313 =
________
44.30 =
_________
1.1233 =
EX1-27 (of 28)

28. MULTIPLYING AND DIVIDING MEASUREMENTS
Exact technique – The answer’s RELATIVE tolerance is the sum of the RELATIVE tolerances of each measurement
(0.313 ± L)(44.30 ± 0.03 atm)
____________________________________________
( ± L)
= atm
Relative tolerance for answer =
Actual tolerance for the answer = (answer)(relative tolerance)
= ( )( ) =
= 0.09
Answer = ± 0.09 atm
EX1-28 (of 28)