Mass
Volume
Area
Length
Quantity
2.54 cm (exactly)
30.48 cm (exactly)
0.914 m
1.609 km
0.0929 m2
0.946 L
28.3 L
0.454 kg
1 ft
1 yd
1 mi
(100 mi)
1 ft2
1qt
1 ft3
1 lb.
(2 lb.)
With Three or More Digits
1 in
(4 in)
English System
Unit
0.5 kg
(1 kg)
28 L
1 L
0.1 m2
1.6 km
(160 km)
1 m
30 cm
2.5 cm
(10 cm)
With One or Two Digits
Value in Metric System
English Units Compared to Metric Units
1 dm2 = 1 dm × 1 dm = 10 cm × 10 cm = 100 cm2
4 in × 4 in = 4 in ×
2.54 cm
1 in
× 4 in ×
2.54 cm
1 in
≈ 103 cm2
SIGNIFICANT DIGITS IN MEASURED AND EXACT QUANTITIES
1. Indicate whether each of the following is a measured (M) or an exact (E) quantity.
5 books _____________________
5 lb
_____________________
9.25 g
_____________________
0.035 kg _____________________
12 roses
_____________________
16 ounces in one pound _____________________
361 miles
_____________________
1000 m in 1 km _____________________
2. State the number of significant figures in each of the following quantities.
6.5 g
_____________________
0.018 g
_____________________
0.00608 g
_____________________
$2,546, 000 _____________________
1.360 mL
_____________________
655 million beans _____________________
4.5 m
_____________________
204.25 g
0.0004 L
_____________________
6.25×105 mm _____________________
805 lb
_____________________
34.80 km
_____________________
2.50×10 – 3 L _____________________
8×105 g
_____________________
1200 km
250. mL
_____________________
_____________________
300.0 L
_____________________
3.9800×1010 atoms _____________________
_____________________
1500 meter freestyle swimming _____________________
SCIENTIFIC NOTATION
1. Perform the following mathematical operations without using a calculator.
102 × 105 = _______
10 2
= ________
10 4
10–24 × 105 = _______
10 −3
= ________
10 −6
1016 × 10–5 × 10–11 = _______
10 5
= ________
10 −10
10 −4
= ________
1018
2. Write the following numbers in scientific notation.
93 million _____________________
760000000 (3 sig. figs.) _____________________
0.0001206 _____________________
0.00000450 _____________________
0.00130
0.055×1010 _____________________
_____________________
4,450,000 (4 sig. figs.) _____________________
0.00032
_____________________
38,000
25.2
_____________________
0.0505
_____________________
_____________________
0.0000000021 _____________________
3. Write the following numbers in scientific notation.
0.0102×10–3 _____________________
1.9912×10–5 _____________________
4551×104
0.08178×10–3_____________________
_____________________
6022×1020 _____________________
27.21×10–4
_____________________
4. Write the following as standard decimal numbers.
4.09×102
3.00×10–4
_____________________
5.315×101 _____________________
8.2×10–3
_____________________
3.150×103 _____________________
2.46×10–6
_____________________
_____________________
METRIC PREFIXES
1. Fill the blanks in the table.
milli-
Prefix
10n
μ
n
Symbol
kilod
10‒12
10‒2
2. Perform the following unit conversions by moving the decimal point.
123 cm =
m
134000 m =
μg
0.0000000206 g =
km
12 mL =
L
50 mg =
g
3600 J =
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 =
μg
536 μL =
mL
1.33×103 nm =
7.82×108 g =
pm
kg
265 nm =
4.365×1010 cm =
nm
8.209×106 km =
dm
4. Fill the blanks.
1 yd =
ft
m
1m =
cm
1 yd2 =
ft2
(1yd × 1yd square)
1 m2 =
cm2
(1m × 1m square)
1 yd3 =
ft3
(1yd × 1yd ×1yd cube)
1 m3 =
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 =
dm3
0.078 pm2 =
mm2
7.09×1015 cm3 =
μm3
3.67×1019 mm3 =
nm3
135600 dm2 =
km2
1.35×109 cm3 =
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
3.20×105 cm
6.9×10−8 km
0.405
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
3.20×105 dm3
6.9×10−8 cm3
0.00601 L
mL
lliM.!2..Read im...English and Metric Ruler
Illustration llf.m English .aruill..metric measurement
Example English
measurement
{
certain
"digits"
uncertain
(doubtful)
"digit"
/'-...
I
*4" + 314" + 0.5116"
•The following are aleo valid
fractional notation measurements.
4 11 + 6/8 11 + 0.5/16"
I
4 11 + 12116 11 + 0.5/16"
Some rulers will be
1"
calibrated to '32
.
411 + 12.15/16 11
English---+->-
Centimeters
II
,
5 cm+ 0.5 cm+ 0.08 cm = 5.58 cm
Example metric{
measurement
50 mm + 5 mm + 0.8 mm
'-----certain
/
I
= 55.8mm
uncertain
(doubtful)
digits
digit
Conversion ll.( Fractional English Measurements tQ. Decimal Engljsh Yiilues
,------------ ...
--
I
-
--
- -
411
+
314"
+
0.5116"
Decimal
4"
+
0.75"
+
0.03125"
Decimal
4"
+
0.75"
+
0.03"
Fractional
I
I
I
I
"-----i------Certain 11 digits" give
an unlimited number
of significant figures.
...
"--·i----
=
4.78"
I
Uncertain (doubtful) "digits" give a limited number
of significant figures. The doubtful digit here limits
the decimal answer to the hundreths place.
English Units Exercise
Measurement
Fractional Notation
Example
A.
B.
C.
D.
E.
F.
4" + 3/4" + 0.5/16"
Decimal
Value
4.78"
Significant
Figures
3
Place of
Doubtful Digit
0.0X
Metric Units Exercise
Measurement
Example
G.
H.
I.
J.
K.
L.
Value
cm
5.58
mm
55.8
Calculation Exercise
English Units
Number Place of
Calculation
Answer
of Sig. Doubtful
Figs
Digit
F−E
F×E
D+E+F
C−A
C/A
D/F
Significant Figures
cm
mm
3
3
Calculation
L−K
I×J
G/H
K3
(K – J) / H
I/J
Place of Doubtful Digit
cm
mm
0.0X
0.X
Metric Units
Number Place of
Answer
of Sig. Doubtful
Figs
Digit
-
-~-----------------------------------
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
~-----------!
~ -----------1
~ } ____28.3 mL -
25
25
~ - -20 --- -30
I
35
15
40
10
45
5
Example measurement
- - - 0.3 mL estimated and read ku;t
- - - - - - - +3 m.L read serond ·
------ +25 mL read first
28.3 mL
------1
~----------i
I
<
All meniscuses should be read at the middle - in the
case of graduated cylinders the bottom of the meniscus.
+ - t - - - - Two types of 10 mL Graduated Cylinders
e
10
1=~
·----------i. .______,
4---= fi
' 5-- = 5 ·---------- J!.__ _ _ ____.
~
3
===
7
===
~
===
--
5
1=;; 3~ ----------i._____
-6 -- 4
-7 -- 3
--- 2
8
-9 -- 1
o==== z
f..o=..t
·----------4._________,
----(0.6) of0.2 mL = 0.12 mL estimated and read [cut
4 - - · ;:5:::::::
- - - -_.,. ______
6===.::::= 4
__J
~ 6.32 mL ._... Example measurement
+0.2 mL read seeond
_..±l!.. ____!!!L.. read first
6.32 mL
5
·----------i
. _----
--- ----I
I
I
~
~
~
,,,
~
RULER EXERCISE
Length
Object
name
cm
(decimal
notation)
in
(decimal
notation)
in
(fractional notation)
Line 1
Line 2
Line 3
Line 4
Line 5
Average Experimental Value for cm/in Ratio:
Accepted Value for cm/in Ratio:
Percent Error =
2.54 cm/in
│Exp. Value – Accepted Value│
Accepted Value
×100% =
Line 1
______________________
Line 2
__________________________________
Line 3
________________________________________________
Line 4
__________________________
Line 5
_______________________________________
cm/in
(decimal
notation)