SIGNIFICANT DIGITS IN MEASURED AND EXACT QUANTITIES
1.
2.
Indicate whether each of the following is a measured or an exact quantity.
5 books
exact
12 roses
exact
5 lb
measured
16 ounces in one pound
exact
9.25 g
measured
361 miles
0.035 kg
measured
1000 m in 1 km
measured
exact
State the number of significant figures in each of the following quantities.
6.5 g
2 s.f.
300.0 L
4 s.f.
0.018 g
2 s.f.
3.9800×1010 atoms
5 s.f.
0.00608 g
3.s.f.
$2,546, 000
4 s.f.
1.360 mL
4 s.f.
655 million beans
3 s.f.
4.5 m
2 s.f.
204.25 g
5 s.f.
0.0004 L
1 s.f.
6.25×105 mm
3 s.f.
805 lb
3 s.f.
34.80 km
4 s.f.
2.50×10 – 3 L
3 s.f.
8×105 g
1 s.f.
1200 km
2 s.f.
250. mL
3 s.f.
1500 meter freestyle swimming
4 s.f.
SCIENTIFIC NOTATION
1.
Perform the following mathematical operations without using a calculator.
102 × 105 = 107
10–24 × 105 = 10–19
10 −3
= 103
−6
10
10 2
= 10–2
4
10
2.
4.
10 −4
= 10–22
18
10
10 5
= 1015
−10
10
Write the following numbers in scientific notation.
93 million
9.3×107
0.0001206
1.206×10–4
0.00000450
4.50×10–6
0.00130
1.30×10–3
0.055×1010
5.5×108
0.00032
3.2×10–4
760000000 (3 sig. figs.)
4,450,000 (4 sig. figs.) 4.450×106
3.
1016 × 10–5 × 10–11 = 1
7.60×108
38,000
3.8×104
25.2
2.52×101
0.0000000021
2.1×10–9
0.0505
5.05×10–2
Write the following numbers in scientific notation.
0.0102×10–3
1.02×10–5
1.9912×10–5
1.9912×10–5
4551×104
4.551×107
0.08178×10–3
8.178×10–5
6022×1020
6.022×1023
27.21×10–4
2.721×10–3
Write the following as standard decimal numbers.
4.09×102
409
3.00×10–4
0.000300
5.315×101
53.15
8.2×10–3
0.0082
3.150×103
3150.
2.46×10–6
0.00000246
METRIC PREFIXES
1. Fill the blanks in the table.
Prefix
kilo-
deci-
centi-
milli-
micro-
nano-
pico-
k
d
c
m
μ
n
p
103
10‒1
10‒2
10‒3
10‒6
10‒9
10‒12
Symbol
10n
2. Perform the following unit conversions by moving the decimal point.
123 cm = 1.23 m
134000 m = 134 km
50 mg = 0.05 g
0.0000000206 g = 0.0206 μg
12 mL = 0.012 L
3600 J = 3.6 kJ
3. Perform the following unit conversions by moving the decimal point and/or by changing the
power of 10. Write the final result either in decimal or in scientific notation which ever seems
to be most appropriate in terms of presentation of the final result.
2.98×105 g = 29.8 μg
7.82×108 g = 7.82×105 kg
265 nm = 2.65×107 m
536 μL = 0.536 mL
4.365×1010 cm = 4.365×103 nm
1.33×103 nm = 1.33 pm
8.209×106 km = 0.08209 dm
4. Fill the blanks.
1 yd =
3 ft
1m =
102 cm
1 yd2 =
9 ft2
(1yd × 1yd square)
1 m2 = 104 cm2
(1m × 1m square)
1 yd3 = 27 ft3
(1yd × 1yd ×1yd cube)
1 m3 = 106 cm3
(1m × 1m × 1m cube)
5. Perform the following unit conversions by moving the decimal point and/or by changing the
power of 10. Write the final result either in decimal or in scientific notation which ever seems
to be the most appropriate in terms of presentation of the final result.
569 cm3 = 0.569 dm3
0.078 pm2 = 7.8×1020 mm2
7.09×1015 cm3 = 7.09×1027 μm3
3.67×1019 mm3 = 0.367 nm3
135600 dm2 = 0.001356 km2
1.35×109 cm3 = 1.35×109 mL
6. Complete the table by performing unit conversions. Use scientific notation for numbers that
have more than three leading or tailing placeholder zeros.
mm
cm
dm
km
3.20×106 mm
3.20×105 cm
3.20×104 dm
3.20 km
6.9×10─2 mm
6.9×10─3 cm
6.9×10─4 dm
6.9×10─8 km
40.5 mm
4.05 cm
4.05×10─5 km
0.405 dm
7. Complete the table by performing unit conversions. Use scientific notation for numbers that
have more than three leading or tailing placeholder zeros.
m3
dm3
L
cm3
mL
3.20×102 m3
3.20×105 dm3
3.20×105 L
3.20×108 cm3
3.20×108 mL
6.9×10─14 m3
6.9×10─11 dm3
6.9×10─11 L
6.9×10─8 cm3
6.9×10─8 mL
6.01×10─6 m3
0.00601dm3
0.00601 L
6.01 cm3
6.01 mL
English Units Exercise
Measurement
Example
A.
B.
C.
D.
E.
F.
Fractional Notation
4" + 3/4" + 0.5/16"
1/4" + 1/8" + 1/16" + 0.3/16"
3/4" + 1/8" + 1/16" + 0.3/16"
1" + 1/2" + 1/16" + 0/16"
2" + 0.6/16"
3" + 3/4" + 1/8" + 1.9/16"
4" + 1/2" + 1/8" + 0.5/16"
Decimal
Value
4.78"
0.39"
0.96"
1.56"
2.04"
3.99"
4.66"
Significant
Figures
3
2
2
3
3
3
3
Place of
Doubtful Digit
0.0X
0.0X
0.0X
0.0X
0.0X
0.0X
0.0X
Metric Units Exercise
Measurement
Example
G.
H.
I.
J.
K.
L.
Value
cm
5.58
0.65
2.00
3.49
10.00
11.26
13.61
mm
55.8
6.5
20.0
34.9
100.0
112.6
136.1
Calculation Exercise
English Units
Number Place of
Calculation
Answer
of Sig. Doubtful
Figs
Digit
F−E
0.67±0.02 in
2
0.0X
2
F×E
18.59±0.09 in
4
0.0X
D + E + F 10.69±0.03 in
4
0.0X
C−A
1.17±0.02 in
3
0.0X
C/A
4.0±0.1
2
0.X
D/F
0.438±0.003
3
0.00X
Significant Figures
cm
mm
3
3
2
2
3
3
3
3
4
4
4
4
4
4
Place of Doubtful Digit
cm
mm
0.0X
0.X
0.0X
0.X
0.0X
0.X
0.0X
0.X
0.0X
0.X
0.0X
0.X
0.0X
0.X
Metric Units
Number Place of
Calculation
Answer
of Sig. Doubtful
Figs
Digit
L−K
2.35±0.02 cm
3
0.0X
2
I×J
34.9±0.1 cm
3
0.X
G/H
0.325±0.007
3
0.0X
3
3
X
K
1428±4 cm
4
(K – J) / H 0.63±0.01
2
0.0X
I/J
0.349±0.001
3
0.00X
-
-~-----------------------------------
ineasur-eme.nt-4
How to Read Graduated Cylinders
All meniscuses should be read at the middle - in the
case of graduated cylinders the bottom of the meniscus.
~
50 mL Graduated Cylinder
~-----------1
----------50
0
~
5
45
10
40
~
15
35
20
30
~
25
25
~-----------!
I
20
35
15
40
10
45
5
48.5 mL
~ -----------1 38.2 mL
} ____28.3 mL - - - 0.3 mL
- - - - - - - +3 m.L
- - - - - -+25 mL
28.3 mL
~ "- - -
30
≈ 55 mL
--- --
Example measurement
estimated and read ku;t
read serond ·
read first
------1
23.0 mL
~----------i
4.2 mL
I
10
4---= fi
1=~
e
9.55 mL __,
·----------i. .____
+ - t - - - - Two types of 10 mL Graduated Cylinders
7
o==== z
1.00 mL
·----------4._________,
__J
1=;; 3~ ----------i._____
3.35 mL
5
-6 -- 4
-7 -- 3
--- 2
8
-9 -- 1
===
--
5
f..o=..t
~
===
===
8.56 mL
9.50 mL
~
1.40 mL
6.32 mL
--- ----I≈ 0.3 mL
·----------i
. _----
+0.2 mL read seeond
I
I
_..±l!.. ____!!!L.. read first
----(0.6) of0.2 mL = 0.12 mL estimated and read [cut
~ 6.32 mL ._... Example measurement
4 - - · ;:5:::::::
- - - -_.,. ______
3
6===.::::= 4
' 5-- = 5 ·---------- J!.__5.65
mL
__
____.
<
All meniscuses should be read at the middle - in the
case of graduated cylinders the bottom of the meniscus.
~
,,,
~
~
~
RULER EXERCISE
Length
Object
name
cm
(decimal
notation)
in
(decimal
notation)
in
(fractional notation)
cm/in
(decimal
notation)
Line 1
5.84
2 + 1/4 + 0.9/16
2.31
2.53
Line 2
9.02
3 + 1/2 + 0.7/16
3.54
2.55
Line 3
12.76
5 + 0.2/16
5.01
2.55
Line 4
6.90
2 + 1/2 + 1/8 + 1/16 + 0.3/16
2.71
2.55
Line 5
10.34
4 + 1/16 + 0/16
4.06
2.55
Average Experimental Value for cm/in Ratio: 2.55 cm/in
Accepted Value for cm/in Ratio:
Percent Error =
2.54 cm/in
│Exp. Value – Accepted Value│
Accepted Value
×100% = 0.4%
Line 1
______________________
Line 2
__________________________________
Line 3
________________________________________________
Line 4
__________________________
Line 5
_______________________________________