# Unit 3 - Introduction - Scientific Notation and SI

```Grade 9 Academic Science - Chemistry
Scientific Notation
What is this number?
 300 000 000 m/s
 0.000 000 000 753 kg
These numbers are very hard to write. A method has been developed to express very large or small
numbers. The method is called scientific notation.
Scientific notation is based on powers of the base number 10. The number 300,000,000 is written
as 3.0 X 108
The first number 3 is called the COEFFICIENT. It must be greater than or equal to 1 and less than 10.
The second number is called the BASE. It must always be 10 in scientific notation. The base number 10 is
always written in exponent form. In the number 3.0 x 10 8 the number 8 is referred to as the exponent or
power of ten.
To write a number in scientific notation, a decimal is put after the first digit and zeroes are dropped.
 The coefficient in the number 123,000,000,000 is 1.23
 To find the exponent count the number of places from the decimal to the end of the number.
There are 11 places In 123,000,000,000.
 Thus, 123,000,000,000 is 1.23 X 1011.
Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as
1.23E+11 or as 1.23 X 10^11.
Numbers smaller than 1 will have a negative exponent. A millionth of a second (0.000001) is 1.0E-6 or
1.0^-6 or 1.0 X 10-6
Scientific Notation Practice
2,700,000
= 2.7 X 106
260
=
0.16
=
0.965
=
34,657,000,000 =
0.124,000,000
RULE
=
+ exponential
- exponential
Extremely large and small numbers are difficult to record in full. A standardized reporting format is used
called scientific notation.
1. The distance between Mercury and the Sun is 5.8 X 10 7 km. It is not written as 58 000 000 km. What
does 107 mean?
2.
What is the effect on the exponent by moving the decimal place in the following direction?
…to the left __________________________
…to the right _________________________
3.
Rewrite the following measurements in scientific notation.
a) 0.000045 km
b) 90 200 s
c) 0.0076 cm
d) 290 000 N
e) 0.000042 km
f) 20 s
g) 0.0623 W
h) 456 000 000 g
4.
Rewrite the following in full.
a) 0.56 X 10-4
b) 3 X 100
c) 3.4 X 10-3
d) 1.6 X 102
e) 9.4 X 104
The Metric System (SI) Rules for SI System of Units
Correct
Incorrect
1.
Leave a space between the number and the unit
75 cm
75cm
2.
No periods except at the end of a sentence
4.5 g
4.5 g.
3.
Put numbers and symbols together
6 kg
six kilograms
6 kilograms
six kg
4.
Use decimals, not fractions
1.5 L
1&frac12; L
5.
Always put a zero in front of the decimal for numbers
less than one.
0.0025 cm
.0025 cm
6.
Group digits in threes for long numbers. Do not use
commas.
14 091.205 s
14,901.205 s
7.
Do not put “s” after the unit symbol.
10 kg
ten kilograms
10 kgs
Find the SI errors and correct for following statements
a. The ribbon was 90cm long
b.
The sun is 150,000,000 kms away
c.
The flash in the sky lasted 1 &frac14; s.
d.
Simon weighed 52 g. last time he checked.
e.
In Canada, one pound is equal to 0.43559237 kilograms
f.
Each candy costs \$ .35.
Significant Digits / Figures
Significant figures are critical when reporting scientific data because they give the reader an idea of how
well you could actually measure/report your data.
The Rules
 ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.
 ALL zeroes between non-zero numbers are ALWAYS significant.
 ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of
the number are ALWAYS significant.
 ALL zeroes which are to the left of a written decimal point and are in a number &gt;= 10 are
ALWAYS significant.
 Zeroes placed BEFORE other digits are NOT significant (e.g., 0.046 has two significant digits)
A helpful way to check the last two rules is to write the number in scientific notation. If you can/must get
rid of the zeroes, then they are NOT significant.
Examples: How many significant figures are present in the following numbers?
Number
Significant Digits
Explanation
48,923
5
3,967
4
900.06
5
0.0004
1
8.1000
5
6
1
501.040
6
10.0
3
3 X 10
All non-zero numbers
Significant Digits
Identify the number of significant digits in the following examples
3560.39
SD =
356.0
SD =
356
SD =
0.0125
SD =
0.01250
SD =
Identify the number of significant digits in the following examples.
 0.0000067
 2001
 3.60
 4.3 kg
 200 393 cm
 0.0073 g
 0.0050 Tbytes
When quantities are being added or subtracted, the number of decimal places (not significant digits) in the
answer should be the same as the least number of decimal places in any of the numbers being added or
subtracted.
Example:
5.67
1.1
0.9378
7.7
2 decimal places
1 decimal place
4 decimal places
Thus, the answer has only one decimal place
Metric Prefixes and Conversions
Like most of the world, Canada uses the metric system of measurement. We know the common metric
prefixes such as centimeter, kilogram and liter. Yet, there are many more prefixes, and in science, the scale
of measurement can be very large or very small.
Metric Prefixes
Prefix
Symbol
Measurement
(order of magnitude)
Actual Value
Example
tera
T
1 X 1012
1 000 000 000 000
terameter
giga
G
1 X 109
1 000 000 000
gigameter
mega
M
1 X 106
1 000 000
megameter
kilo
k
1 X 103
1 000
kilometer
hecto
h
1 X 102
100
hectometer
deca
da
1 X 101
10
decameter
BASE
UNIT
g
L
m
s
1 X 100
1
gram
liter
meter
second
deci
d
1 X 10-1
0.1
decimeter
centi
c
1 X 10
-2
0.01
centimeter
milli
m
1 X 10-3
0.001
millimeter
micro

1 X 10
0.000 001
micrometer
nano
n
1 X 10-9
0.000 000 001
nanometer
pico
p
1 X 10-12
0.000 000 000 001
picometer
-6
Give the metric abbreviation for the following
meter
decigram
microsecond
kilogram
millimeter
megameter
nanosecond
teragram
milliliter
centiliter
decaliter
picogram
What is the numeric meaning of each metric prefix?
mega
centi
deca
deci
milli
nano
kilo
tera
giga
Convert the following metric units
 100 m = _______________________ km

62.5 L = _______________________ cL

485 kg = _______________________ g

0.006 m = _____________________ mm

4.23 km = ______________________ Gm

0.24 cm = ______________________ mm

0.24 cm = ______________________ Mm

5 000 L = ______________________ kL

705 ns = _______________________ s

1.5 ML = ______________________ kL

450 Tbytes = ___________________ bytes

0.003 m = ______________________ cm
large to small
move decimal to the right
small to large
move decimal to the left
Measurement and Significant Figures
Task - Suggest the best unit to measure each line below, estimate the length of each line and record these in
the table below. Then, carefully measure each line below and complete the table (use proper
significant figures).
1
2
3
4
5
6
Line #
1
2
3
4
5
6
Line 6 width
Text
thickness
Text page
length
Floor tile
width
Best Unit
Estimated Length
(L1)
Measured Length
(L2)
Difference
(L2 – L1)
% Error
= (L2 – L1) / L2 X 100
Measurement, Conversion and Significant Figures
Unit Conversions
 Time
 Distance
1 h = 60 min, 1 min = 60 s
1 km = 1000 m
Conversion Examples
Convert 4 h to seconds
1 h = 3600 s (Conversion Factor)
4 h X 3600 s/1 h = 14400 s
Convert 5.2 km to metres
1 km = 1000 m
5.2 km X 1000 m/1 km = 5200 m
Convert 25 m/s to km/h
1000 m = 1 km
3600 s = 1 h
25 m/s X 3600 s/1 h X 1 km/1000 m = 90 km/h
Practice
1. Convert 156 km/h to m/s
2.
Convert 100 m/s to km/h
3.
Convert 75 km/h to m/yr
4.
Convert 170,000 mm/s to m/s
5.
Convert 75 cm/ns to Gm/day
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